You can also just go to the files and drag them in.

Thank you for your suggestion but I tried that and when I inserted the file into the timeline and hit play, I received an error message similar to the one you might get if a clip required rendering, although, the usual colored (un-rendered) bar was absent. This response caused me to suspect that Calibrated Q was not working properly.

There are quite a few variables to troubleshoot.

The Calibrated plugin is a quicktime plugin, and if it's installed it's in /Library/Quicktime/CalibratedMP4EXQ.component (and there's another one as well, I think 2 calibrated components are installed there.)

If those components are there (you could try restarting your computer if they are)

If you use Quicktime Player to try to play the .MP4 file (the demo version truncates any clip to 30 seconds) what happens? If it plays in QT then just try playing the clip in FCP's viewer, rather from a sequence. If that plays fine then it could be that your sequence isn't set up the same as your clip.

Hope this helps.