Sometimes your pet may be in pain but unable to tell you. I know they say cats hide when they are in pain because they think someone is hurting them. That really isn't true if they are intelligent enough. I think they are just being irrational like a human would be in that situation. But some of the slower-witted ones (ones that do things like sit in their food dish) might not understand.
LOL! Yes, cats don't want anyone to know they're hurt cause they're more vulnerable. Cats know that hurt animals make good prey, being predators themselves. Cats will sometimes purr when they are hurt which may lead one to think they're OK. They purr to calm themselves. It might also help with healing as a purring cat can work wonders! I think when a cat purrs it like they're OMing. They're sending out peaceful vibes to the world.