If the website http://www.stationindex.com/tv/tv-markets
is reliable, I have found in the top 20 markets that:
LA has channels 7 and 8, but one is low power digital
Miami and Phoenix have both channels at full power, BUT there is a big difference between the power output of the two channels.
I think the Great Falls, MT market may be unique - with the two channels being broadcast from exactly nearly the same location with almost the same power. I suspect that this is somehow not working for the TiVo box and causing reception issues on one channel. TiVo has not heard about it before because I may very well be the first person trying to use this Premier for OTA broadcasts in this environment.