Man, what a useless thread. Egos, people, egos!
The MTS format is bullshit. It’s not that AVCHD is a problem, it’s just that it deserves to be encoded natively with all the metadata and such included—for example, with “log and transfer” within FCP. But often clients are in Indonesia or some shit and email you MTS files and that’s just the way it is.
I’m going to offer up my solution, ugly as it may be. Go ahead and use AME to encode the .mts file. Set it to export at the resolution and codec you want. So now you have a perfectly good video file with no audio.
Next, open the original .mts file in the VLC player (which I’m assuming you have.) Run a program like WireTap Pro or Audio Hijack to capture the audio from the VLC player. I assume your MTS file is not the most hi resolution audio, so don’t get all cringy. Now save your audio as something decent (aif or aac) and then open both files up in a video editor. I chose not to use FCP, but instead FCPX, because it works like iMovie—quick and dirty—no setting scratch disks, etc. and I’m not keeping this project file anyway.
Now just import your silent video and drop it in the timeline. Import your audio file and do the same. Sync it up, export to ProRes and you’re good to go in FCP. Does that make sense?
It’s not pretty, but we’re talking about either saving the file, and making it editable, or complaining to the client that their footage sucks. Up to you.