Congrats on getting three in one day, and at some great places, too! I keep waiting for a big day like that but they only seem to trickle in...
I also applied to too many and am still waiting for many of my top choices. At this point I wish they would just let me know one way or the other so I could finalize travel plans and such.
Anyway, I would agree with you that there is some method to it, but only in a general sense. I think there are probably some basic cutoffs that all the elite programs use, so if one is below those standards then he/she may be out of luck for all of the elites or may just get a few of them. An outstanding applicant who meets all of these standards will, in general, get more interviews at the elites than a mediocre applicant. However, being outstanding doesn't seem to guarantee interviews at all the elite programs, and 2 applicants who appear similarly outstanding may both have a handful of interviews from the most competitive programs, but they may be to entirely different places. That is the part that seems random to me.
Also, I think the timing is an important factor. Most of the elites don't have a need to send invites so early - what does MGH have to lose by waiting until mid-November? They know they can get enough great interns without rushing it. It is hard to know at this point whether we aren't going to ever get invites from the best places or if they are just taking their time.