Taking what isn't yours is a little goofy for if we aren't separate, then what is really ours? I'm intrigued to see giving and stealing in the same precept, almost as if these are opposites. Stealing is taking what is not yours, as is receiving. In one case the giver is compliant, in the other she is not.
Maybe giving is like a rush of water. If one is busy giving they won't have time to steal, where the water reverses it course. I don't know.