EA still "took" these games away from them.
no they didn't. they didn't take anything away from these companies, because the publisher doesn't own the IP, the developer does.
If Acclaim owned the IP for Burnout, then EA would have 'taken' the game. But Criterion shopped around after Burnout 2 was complete. I'm sure they talked to other publishers, as did Free Radical (i know for a fact they did) and figured out what was best for their company.
You are not taking into consideration that perhaps the developers who own these IP didn't
WANT to work with their previous publisher. How would that be considered take, when again all the power is held by the developer who owns the IP, not the publisher.
What EA did with Origin, or Westwood. Those would be considered 'take', because EA just bought them out.
One the situation like Stranger, how can EA take something that the original publisher didn't want? MS doesn't care, hell. MS will probably get a check from OI or EA for development costs MS paid for.
EA didn't 'take' anything from the previous publishers. These are games where the developer owns the IP and can do business with whoever they want.