Taking something away from a baby who could hurt themselves might be appropriate, although we just ask first. This most often works. If it's a kid who understands and is not in imminent danger, I'll continue the conversation until I convince the kid that I need the item because it's dangerous. Since I only do this when it's actually dangerous, they believe me.
Cheese in not dangerous. If the 1.5 year old had grabbed the cheese and stuffed it in her mouth, it would not be appropriate. It is also not appropriate for me to do the same thing in her stead. So, yes, I believe grabbing something out of the hand of someone, especially someone smaller than me, to get something they have that I want is snatching. I think modelling that fosters lousy play and stinky behavior. I do not believe that it fosters generousity.
The solution seems so obvious, I don't understand the discussion. Is there a world-wide cheese shortage? When my second got big enough to want the samples too, I accepted that I know had double the number of children...therefore, I needed double the samples.
It took me one or two times of dd2 being on solids to get this. But dd2 is pretty good at letting you know what she needs, so I caught on pretty quick.
I agree with you that it's not ok to grab something away from someone else. i wouldn't do that. I wouldn't yank, snatch, wrench, grapple, snap up, or seize, either. But I WOULD reach over and calmly take it if I asked for it and it wasn't given.
I realize a piece of cheese isn't dangerous, but note I said I also would take something that is 'not allowed'. If my dd had my valuable antique knick knack from my great great grandmother I'd most likely say, "I am concerned that will get broken if we carry it around, can I have it?" If she didn't give it to me I would reach over and calmly take it from her. I wouldn't yank, I wouldn't yell, I wouldn't do anything more than that and then deal with the fall out in whatever manner I could. ("I know you are really upset, maybe there is something else you can play with?")