what video formats can imovie 10.1 use?

Running iMovie 10.1.1 under OS X 10.11.3 on a MacBook Pro11,1. iPhone 5c on iOS 9.2.1.

If I take a video on the iPhone and transfer the file to the Mac, the response is "iMovie cannot open files in the 'QuickTime movie' format".

If I try opening a .m4v video file in iMovie, the response is "iMovie cannot open files in the 'Apple MPEG-4 movie' format".

Both file (and many like them) play just fine in FCPX (I know, I know), the QuickTime player, and a dozen or so other applications,

including Mail.app.

I've already tried deleting iMovie (and related files) and installing it fresh from the App Store.

Seems more than a little pathological.