Dear C.,
You sound like a wonderful mom and a committed caregiver! This little boy, and his parents, are lucky to have found you.
My personal belief is that when people treat behavior with only a punishment/reward approach, they are missing the point. This doesn't mean I don't believe in discipline; kids need to learn the difference between right and wrong. But a child who's misbehaving will continue to misbehave until he learns an *alternative.*
Is this little boy an only child? It sounds like he may have simply never had to learn a constructive way to get what he wants. If he hasn't played much with other children, he may have an idea that all toys belong to him; after all, all the toys in his house belong only to him. No matter how obvious "Can I play with that, too?" may be to an adult, for a preschooler who hasn't had much peer experience, it may simply not be in his vocabulary. This little boy may also be anxious or insecure at your house -- not because you're not doing a good job; just because being in a new place can be stressful for preschool-age children.
Either way, you might want to make a big deal out of getting him to ask for toys rather than hitting. You can enlist your children in this by making it a game: "We're all going to ask each other for things," etc. If this sounds even remotely feasible, try starting the game with something none of the kids really care about, say, a paper plate. They can ask for it in silly voices, pass it to each other very fast, etc. You can then bring in a toy that has just slightly more value to them, and so on. If this shows any sign of working, you can ask his parents to reinforce it at home.
In other words, even if the point we really want to make is "no," what kids often need most is an "instead."
Finally, if this really doesn't work, this little guy may just need to be in a play situation with multiple kids who are older and larger than he is. If he's in a group care setting where there's no way he can get away with hitting, he'll be forced to settle for an alternative. I know of one day care center that does this pretty routinely with children who hit: put them in an older group, sometimes only temporarily. Those kids are usually then too intimidated to hit, and as they observe older children communicating, they learn more constructive ways to get what they want.
That was really long and rambly; sorry. But I hope it helped.
Mira