Well, yes......Piaget's idea of play is a little strange. To clarify, she'll take a toy, run to the other room (which entices Mirage to follow) and then drop it - at which point Mirage takes it and goes. He doesn't actually take it out of her mouth.
I didn't intend to comment on your post (which I'd just skimmed), and I apologize if it seemed that way.
FWIW, I came up with the rule because when the poodles were puppies, Minnie would take every toy/chew/whatever away from Perry. Sometimes she'd snatch it, and sometimes she'd rule by intimidation, but she always wanted everything. I later found out in passing (we were discussing something else) that a very experienced trainer whom I respect has the same rule, so I've stuck with it.