My guess is that Capture One ignores the EXIF orientation tag.
I posted my question at the Phase forums as well, and here's a portion of the response from a Phase staff member: "Use Capture One, and you don't need any other programs." What do you think, maybe just a little bit arrogant!?!
I'm also testing Breeze Browser, iMatch, iView, Bridge, Camera Raw, etc, and all the work I do in Photo Mechanic, including rotations, is recognized by all those other apps. C1 is definitely out of the loop, and perhaps resting on their laurels.
Cheers,
Andrew