Peter:
Ran into the same problem and went to Google - looks like its a fairly common problem with no easy answer (for example: http://www.gypsycreative.com/mts-files-boy-they-suck-but-heres-one-sol ution/ ). Best answer seems to be to look for a converter that can take the MTS file to .mov or quicktime, then run it through encoder.
The only way I solved it was the resident video genius took it home and ran it through his personal production set up (burning incense and chanting the Jobs mantra, no doubt) and brought me a functioning version that converted easily into an f4v and worked perfectly as embedded video.