Nate,
Indeed, all Triumph receivers should be oriented with MMI (buttons) pointed North, AFAIK.
As for the calibration magic, the first thing is the PCO which is sort of the "average" point of orientation-independent reception of signals (the "ghost" is certainly a good word for it). In addition to that offset location, the phase center varies around that non-physical average point depending on signal orientation and frequency too...
Antenna calibration models account for both azimuth and elevation of EACH received signal with respect to an antenna-fixed reference frame. So for any given signal of a given frequency in a given spot in the sky, the receiver expects to apply a particular "correction" to that signal under the assumption that the antenna is oriented in the same direction as the model was developed for.
So if the antenna is modeled with a particular correction value for, say, a signal coming from due north at 30 degrees elevation, the only way it can apply the proper correction is if the antenna is oriented so the signal is hitting the antenna at that physical orientation, since the antenna/receiver doesn't measure the orientation of the signal itself. If the antenna is turned away from the expected reference orientation, the signal is still spatially coming from due north, 30 degrees elevation, but hitting the antenna in some other antenna-referenced direction. The receiver "hopes" the antenna is oriented correctly, looks up the azimuth/elevation of that satellite, and applies the expected correction from the model, but in this non-north-oriented antenna example the signal is now hitting the antenna at some other direction which would have a different correction that it
should apply if only it "knew" it was oriented away from north.
That's where a magnetic determination of the antenna orientation could be immensely handy. Now the receiver knows how far off of North it's pointed, and can "simply" add/subtract that azimuth to it's lookup table to find the ACTUAL correction that it should apply for any given signal, no matter how the antenna is pointed... Realistically, one might imagine that, since PCV is dependent largely on elevation angle, tilt corrections should be applied to the calibration lookup in a similar manner as well, if out-of-level shots are being taken.
All of that said, in theory, for sufficiently similar base/rover antennas over sufficiently short distances, orienting both antennas in the same direction (South, or West, etc...) may indeed "self compensate" in a manner of speaking - in other words both receivers would apply the same "wrong" correction, yielding absolute positioning errors while giving adequately good relative measurements (all your measurements are for example now off by 5mm to the East, but it's the SAME 5mm East error for both receivers...). However, over the course of a day, as satellite locations change and different "wrong corrections" are applied to the signals, repeatability of measurements may get funky.
Hopefully someone can point out any errors in that whole monologue there. I'm no electronics/RF/NGS engineer
Anyway, for the time being, I quite happily spin my T-1 on the stick so that the lights and buttons are pointed north and mentally announce "Northern Lights" as part of my pre-shot checklist. "Look south, young man - that's the way it's always been done!" to squeeze out those extra mm of accuracy.