I think it is a learned behavior from day care centers, I worked for a few crappy centers. They learn biting, hitting and snatching as a way to deal with other kids. The problem is in some day care centers is that you have 1 teacher to a lot of kids, so say the kids are 1 then it is 1 teacher to 5 kids, then at 2 it is 1 teacher to 7 kids, then at 3 it is 1 teacher to 10 kids. The kids basically are being raised in a heard. They don't get much 1 on1 attention unless they do something wrong so they learn to do these things to keep a toy the want to play with or to protect themselves.
I think you should seriously look into he center your child is at, look at how many kids are left with 1 adult and drop in unannounced at different times of the day. If you find everything is fine then chances are it is an age things and she will grow out of it. If not then you may want to find a center where they have less kids to 1 person.
Good luck whatever you decide to do.