Yes, DirectShow (which, in this case, is what's used by Windows Media Player) simply tries to open it with just about any codec you have installed on your system until one of them succeeds. Other players just look at the file extension and use what would be appropriate.
But still, if the software you used to encode it to MP3 saved it with a WAV extension I'd have a nice, long talk with it and convince it to stop doing that - "Bad software, baaad... Sit. Fetch. Save as MP3."
np: Michael Fakesch - Diesehle (Marion)