QED:

Actually, the front crawl (what we typically think of freestyle) must be swum in the freestyle portions of the Medley events (individual & relay).

And it's "doggie-paddle", not "doggie-style". Not that I wouldn't want to try that anyway.

I think the rule in an IM or medley relay is that you can do any stroke other than backstroke, breaststroke or butterfly; i.e. you don't have to do the forward crawl. Being both a swimming nerd and a lawyer, I have always wondered if you could get around this rule by swimming an illegal butterfly -- a couple of strokes with a one-arm recovery, or finishing with a one hand touch.