Okay from my quick research, it looks like you need to import MTS files with the dialog "Import from camera" instead of just import files.
However if none of this works I'd take the Streamclip route. Technically, yes, any video conversion is going to degrade the quality of your footage, but there's no way around it and the loss will be completely imperceptible to your (or anyone else's eyes). Repeat that conversion 1000+ times then that's a different story.
Squared 5 will absolutely not take (or even be aware of) your footage if you use Streamclip. If you're concerned about it, though, disable your Internet connection during the duration of your file conversion. But I guarantee you, they won't steal anyone's footage nor would they have any need to.
If you want quality, I would recommend converting to ProRes 422 (HQ) at 100% quality with no scaling enabled.