I'll take a look at some of those statements and go through why those are wrong and what you should really do.
"Never praise or reward a dog who is behaving fearfully, nervously or is displaying anxiety".
The idea behind this statement, is that you could then reward the dog for this behaviour, which would increase the frequency of the behaviour.
But, fear is an emotion - you can't increase the frequency of displays of fearful behaviour, by giving positive reinforcements, because those behaviours are caused by the underlying emotion. That isn't how it works.
You COULD reinforce fear by adding more scary things - if a dog is frightened of a person and then that person shouts or hits or kicks the dog - that would increase the dogs fear of people.
That is pretty obvious - but this ones less so. If your dog is really scared, and then YOU behave all anxious and tense and edgy you transmit that in your body language and in your voice, then even if your words are 'there there its ok doggy' you could still be reinforcing the fear, because you are adding MORE fear.
Your dog sees you as a secure person to be around, they take some confidence from you, so in the above example, if YOU are acting fearfully, the dog will find that upsetting and this will increase his own anxiety.
It isn't because you attempt to comfort him though, it wouldn't matter what you said or even if you said nothing - its your body language and behaviour he is picking up on.
There are of course times when you would not want to approach a dog to give them a reward or physically touch them to praise them - thats when YOU are the object of their fear. In a situation like that, regardless of your intentions, approaching a fearful dog is dangerous and liable to get you bitten - even if the dog doesn't bite you, you have probably increased his fear, not decreased it by pushing him too far.
"Cesar deliberately confront's [the dogs] fears to build trust"
This is not just wrong, this is dangerous. The idea is to carry on doing something the dog finds frightening until the dog realises it is wrong, and the situation is actually not frightening.
That isn't what actually happens though - what happens is, IF the person involved does not get seriously bitten, the dog realises there is no point objecting or trying to get away, so he shuts down. He exhibits a state called 'learned helplessness' which is when an animal has learned that nothing they can do will stop the scary thing happening, so they stop trying.
It does not mean they are no longer frightened, and it does not mean they are relaxed or happy with what is going on - they have just stopped trying to stop it or avoid it.
When this happens with dogs, they effectively learn to fear the person who did this, more than whatever it was they were initially scared of. When you then get a new person to introduce the scary thing, they are likely to react and most likely to react much more violently than before.
In dog terms, the most common example is that a parent or some adult, causes a dog to shut down over some issue, lets say its being brushed.
They then believe because the dog is now not objecting, that the dog is ok to be brushed, and they won't find out differently until someone new tries it. So when their 5 year old picks up the brush one day, the dog errupts, he has NOT learned to fear the CHILD more than the brush, so he reacts and the end result is highly likely to be a badly bitten and frightened child and a euthanised dog.
It IS true that to desensitize a dog to something they are scared of, they will HAVE to be exposed to that thing, but HOW we go about that is very different from the way Cesar suggests.
"Exposing a dog repeatedly to the object he fears can teach him that there is no threat"
As above, this depends on HOW you go about that exposure. Cesar uses flooding, which is continued, confrontational and deeply stressful exposure that results in the dog shutting down. The dog doesn't learn that the object is not a threat, he learns that the person is a bigger threat!
So how do we deal with fear then?
The trick to dealing with fear is understanding stress, and 'safe thresholds'.
Stress is quick to build up, and slow to dissipate - so don't expect to be able to build steady progress day by day. Instead aim for a two steps forwards, one step back approach where you are continually assessing the stress involved and backing off the pressure to let your dog truly relax and unwind.
Your dogs safe threshold is the distance at which he can see something he recognises as scary, but doesn't feel the need to react yet.
These thresholds change as you progress, but to begin with you want the dog to feel as safe as possible.
Lets say your dog is terrified of horses. If he is 10 ft from a horse he barks and lunges and if you try to pull him back on the leash he turns and bites the leash and your leg. He doesn't listen to you and you could wave a roast chicken under his nose, he wouldn't notice.
That is because at 10ft, this dog is massively over threshold, he cannot cope at this distance, he is so far gone it isn't that he doesn't want to listen to you, its that he physically CANNOT listen to you. Nor can he perceive that roast chicken as a reward.
At 30ft away your dog stares at the horse, he doesn't bark or lunge but he still can't listen to you. You can pull him back on the leash and he won't turn and bite it or bite your leg, but he is still ignoring the roast chicken.
At this point, he is still over threshold but not to the point where it is causing a severe reaction. This distance is too close for you to teach him anything good though.
At 45ft away, your dog can see the horse, but he can listen to you a little. He is flicking his attention between you and the horse and he can take a small piece of chicken and eat it. He isn't capable of complying with cues such as sit or down, but if you say his name he will look at you briefly.
This distance is the very edge of his safe threshold, he isn't ready to work at this distance just yet but he might be soon.
At 55ft away, he can still see the horse, but now he can listen to you if you ask him to sit, he is very keen on the chicken and his attention is much more on you and the reward, with occasional glances in the direction of the horse that tell you he is aware of its presence, but he is not too bothered as long as it gets no nearer.
THIS is the distance where you would start to desensitize and counter condition - THIS is the level of exposure that is safe and you can work with.
So you ensure that you never get nearer than this during this stage of training.
You make sure that the horse isn't going to get any nearer (control of the environment - if you don't have it, just avoid the situation, turn around and walk away!).
Now you can mark and reward his looks at the horse, that's all you need do. Horse = pieces of yummy chicken.
What you are looking for now is, over a number of sessions (and not every day please, let those stress levels drop between sessions), his attitude changes, his body relaxes, he can give you his attention for longer periods of time. When he initially sees the horse he should look happier, ask you where the yummies are etc.
When you reliably have that result, ideally in a number of locations, over the course of a few weeks, THEN you can consider reducing the distance slightly.
If you find you get a reaction, or he is obviously uncomfortable, increase the distance - it is key here that you work at the DOGS pace, not any pace you decided you should achieve this at. HE decides when he is comfortable with this scary thing, not you.
By working like this, you can eventually change the dogs emotional reaction to the sight of something he previously considered scary. It works because you classically condition him to associate the sight of something, with a tasty reward (you could also use high value toys here if your dog likes those better).
Depending on the trigger, you may have to work through several other stages - for example, horses move - he could be ok with a horse stood still, or a horse in a stable, but still find a horse moving or a horse being ridden a scary thing. So desensitize those things in the same way.
If your dog is fearful of being brushed, you might start out with rewarding him for seeing a brush on the floor on the other side of the room, and gradually work your way up via brush in your hand, brush touching his chest, right the way to brush touching the most sensitive part of his body.
No part of behaviour modification or training should involve a dog being scared or being bullied into using his teeth to protect himself. A good behaviourist or trainer can read a dogs behaviour and has absolutely NO need to push them any further.
I can see that a dog is food aggressive within 10 seconds of that dog being given a bowl of food - why would I need to push that dog into actually biting, what more would I learn??