I guess I'm the odd one out, but when I nannied similar situations with my son (though I don't know if I started this technique quite so young as a year) I tried to gently give the toy back to the previous owner and say "Right now it's X's turn, but when he/she is all done with it, it can be your turn." very cheerfully and "we don't take things out of other people's hands." or "you can ask if you can have a turn." (i say "gently" as you feel like a big silly trying to tear a doll out a baby's hand while explaining about sharing!) We repeated those phrases A LOT! (and -- at 3yo -- still do, but only very occasionally.)
My reasoning is that I believe that they should, by all means, learn conflict resolution but I think that is an emerging skill for a slightly older child. Toddlers are just starting to figure out proper social interaction. if they don't have a few ground rules about how civil play is supposed to (ideally) work, then the only conclusion they can draw is that stronger, more aggressive people get to do what they want.
I want my kids to know when they are playing alone, that they are entitled to speak up when someone snatches a toy from them and also that it's not ok to snatch from others. I want them to get a sense for "right and wrong" so even when an adult is not there to advocate for them, they know that they have rights.
so we have a set of basic rules like "If it's in your hands, its your turn. but if you put it down and start playing with something else, then it's someone else's turn."