I'm a complete newbie, so I can't be sure, but I don't think that's it. I tried saving it to my desktop, and I changed the .extension to .mp. The file opened in maya, but the scene is blank, and it says "unrecognized file type". If these three things make any difference, then this might hint as to the solution:
I use an iMac
I use the free demo version of Maya 7 PLE
This only happens on some of the models I try to download.
I hope to get the full version when my wallet is a little fatter, since the demo renders suck and there's this little layer over every render saying "Alias Maya 7 PLE" Thanks for the suggestion, anyway.