A lot of CM's methods are based on misunderstanding outdated theories of dog/wolf behavior that have now been scientifically disproven. That said, I've seen the man change and grow over the years. He uses a LOT more positive/reward based techniques (often couched in CM "jargon") in recent shows than in older ones.
When you watch his show, you need to remember that 1. it's entertainment, first and foremost, 2. that you can't make meaningful, long-term changes in a dog's behavior in a half hour, 3. (in fairness to him) he takes on a lot of dogs that most trainers wouldn't touch or have given up on.
If the average person has a real problem with food aggression (resource guarding) with their dog, they should contact a good, positive based trainer, not try to deal with it on their own. They could get hurt. If you are starting with a puppy, it's better to AVOID food aggression, by teaching the puppy to eat out of the owner's hand or with the owner's hand in the food dish on a regular basis. Another method you can (and should) do regularly is to take the dish of "plain old dog food" away momentarily, and return it immediately with something REALLY yummy added to it. This way, the dog will start to think of people taking the dish away as a GOOD thing!
It's never a good idea to do an "alpha roll" to a dog or puppy. All you do is risk damaging you relationship with the dog, and you don't teach them a thing. The reason Miller snapped is that he was defending himself against something he found ver aversive. (having his nails clipped) even though you know it needs to be done. Some dogs are better abut nails than others, but with ALL of them, it's a long, slow process getting them used to it. Kodi was terrible about it. Although he never bit, he struggled so hard to get away that it was simply impossible for me to do by myself. He's almost 3 now, and it still takes our groomer doing the clipping while I stuff cookies in his mouth to keep him calm during the process. I'd love to someday be able to do it at home by myself, but we're not there yet!
So I think that taking yourself out of the loop and having the vet do it can be a good option. Just be careful how much force they are using. I am SURE that part of the reason Kodi got as bad about it as he is, is that when I was having trouble I took him to the vet. When he struggled and screamed, they had two techs hold him down while the vet clipped his nails. This just confirmed in his little fuzzy brain that that nail clipping was a VERY SCARY THING!
It has taken more than two years to undo that experience.