Midori, I don't understand why all your focus on training of a dog is centred around not getting bitten. Are you really that scared of your dogs!
If a dog bites an adult owner, it is because it doesn't understand its place and boundaries within the family.
You bet my dogs get scared of dh when he is is in a temper, they slink of to a safe place (usually under our bed), they would never dream of biting him. It just wouldn't happen.
A nervous bitey dog is an unbalanced dog. Correcting a dog when appropriate, helps sets boundaries and de-stresses the dog, they know someone is in charge and making decisions, so they can relax.
If I tell my dog to sit or put a finger on her bum, she knows that both mean sit. If I say bad dog in a stern voice or swift smack, it means all the same, she knows I am unhappy. One thing is not more abusive to her than the other, what matters to her and makes her sad is that I am not pleased with her and she does the cutest head on my lap, 'I am sorry' look.
If your notion of training a dog means teaching it to dance, by all means use treats. But when it comes to really important stuff, like resource guarding and recall, it requires a calibrated approach of praise and corrections to guide behaviour, depending on the nature of the dog.
My experience is that negative behaviours with regard to important things, such as food (e.g., growling at humans, stealing) are best dealt swiftly with a correction, and they do not become an issue. And once they display the appropriate behaviour, they 'earn' the bone or meal. Our dogs are relaxed about us touching their food, feeding them, giving/ taking bones.
Things like recall work with a combination of praise/treats and correction. Treat or praise when dog comes back on her own. If you have to go and get the dog, a consistent punishment (depending on what the dog values, in our case it is going home, so outing is over) till you get the right behaviour. Recall is really not a problem with our dog at all now, and it is important as we live in farmland and we would be in big trouble if she chased cattle or ran off after sheep.
If training a dog to dance (!) or do tricks, by all means use treats and it is of little importance whether they do a pirouette or decide not to do it.