With children, it is easier to teach them and state why they shouldn't jump all over the dog and they shouldn't be allowed to just because the dog tolerates it so I can agree wholeheartedly there.

With other creatures, it's a bit harder. The Kitten is not going to learn not to do it by being told not to by it's owners or even by being stopped by the owners, it will just go back for more. Cats aren't famous for being obedient creatures anyway. If it was a puppy, it would probably engage in similar behaviour too. Some dogs put up with it and others snap.
If the pittie snapped at the kitten for digging it's claws in too hard, that would probably be the only way it learned. The only other way is to not let the kitten anywhere near the dog and then you get it growing up to not be used to the dog.
In the case of a puppy, it is better to let the pup learn from it's own mistakes and be snapped at. It won't learn respect for the other dog from yourself.

Remember that wolves in the wild often tolerate being mobbed by their pups. They don't do it to please somebody else though like an owner, they do it because the pups are important and their future and they don't want to be attacking them and are protective of them. I've seen countless scenes like this on TV of wild animals being mobbed by their youngsters or the youngsters of another adult who lives with them, having tails, lips, ears pulled and yanked and they just put up with it and these are wild untrained creatures.
The pittie probably noticed her owners were all looking at her and probably smiling too. Thats why she was probably looking back with that look on her face....the same look all the animals tend to have that I've seen tolerating a mob attack from a playful youngster.