This issue is caused by the video files "codec". In order for them to work with iMovie, the file extension you see on the movie file, is not what causes the issue, it is the "internal codec" that you can't see, that does this.
The supported codecs are shown here - TS3356 - iMovie '09: A limited number of video files may require conversion ...
There are literally thousands of codecs out there, so they one you need is anyone's guess. The easiest thing to do, would be to "convert the video" using a video converting software. There are some you can download for free, from the "Apps store". Just open the app's store, and search in the top right for "video converters"
If you need to know the current codec attached to the video, and you can play it back in Quicktime, then open the video in quicktime - window in top menu - show movie inspector - in the "format" area, it should show the codec