I doubt many people are still using this version of iMovie, but I am and I thought I'd share what happened in my case.
In my case, this doesn't have anything to do with iPhoto, because I'm not using iPhoto on this project.
It also doesn't have anything to do with duplicate file names, because I'm quite sure that I had never named any files "pasta with pesto sauce" or "Parmesan on plate with shredder" before, whether inside iMovie or not. 🙂
However, it did work to erase the offending pictures, rename them in the Finder, and re-import them. My guess is that whatever problem had been created in iMovie to create this issue, iMovie has it associated with that particular name. No matter what I did to the picture (moving it, deleting and re-importing, and so forth), the issue remained. But once it's renamed, everything is fine.
Thanks to Bennynormal for the help!