AFAICT, you have copies of the camera cards in AVCHD format.
These are to be considered, for all intents and purposes, as a "camera".
When you do an import, FCP X lets you use the clips right away, but will proceed to import "in the background" (well, not really, because it will only do these "background" tasks when the user is not actively interacting with the program).
It seems that some of these imports did not finish completely.
For these clips, you have to do a File->Import->Reimport from Camera/Archive, and then allow the application enough time to copy them (and, if you have it that way, also transcode them; you probably don't need to create optimized or proxy media).
Press command-9 to see the Background Tasks HUD.
Do not quit the application until you check that all pending operations in the Background Tasks HUD are finished.