Honestly, its has to be a receiver/software issue.
Each tire definitely has a TPS in it (verified visually when a tire was off getting a hole patched). Its possible that some bean counter (like me) could have decided that they could produce 100 more X5s per year by not synchronizing the individual sensors with the receiver. I have to do this manually when I rotate my tires on my V and it takes an additional 2-3 minutes probably.
Also if the person rotating the tires doesn't do this synchronization the driver could get a warning that the driver rear is low, manually check it and determine its fine and then continue driving to the detriment of his passenger front which is actually the one setting off the alarm. Ktono - your first post is what led to my theory, but it appears you then refuted that in your subsequent testing.
I haven't checked operation of the TPMS since the latest software update, perhaps it was one of the changes, maybe I'll check tonight.
Herbert - '12 X5 35d / Sapphire Black / Black Perf Nevada / Aluminum trim / ZPP / ZPS / ZCW / ZAV / Apps / 3rd row
Betty - '04 CTS-V / Black Raven / Black Leather & Suede / 6 speed LS6 combo 400 hp & 400 tq
Sterling - '06 Silverado HD / White / Grey Leather / LBZ Duramax - Allison 6 speed combo / Crew Cab Short Bed LT3