dealer said tire pressure monitor going off all the time is normal (WTF?)

[f5fstop]

Does not fall under state law, in MI that is for those worthless safety inspections that they used to perform on the side of the road (do they still do this?).
TPMS falls under NHTSA ruling, it is a Federal Motor Vehicle Safety Standard (FMVSS). It requires the "passenger cars, multipurpose passenger vehicles, trucks, and buses with a GVWR of 4,536 kilograms (10,000 pounds) or less, except those vehicles with dual wheels on an axle, to be equipped with a TPMS to alert the driver that one or more of the vehicle's tires are significantly under-inflated."

We can thank Ford for this ruling, with some blame on Bridgestone/Firestone, but test reports do show that when the left rear tires were purposly blown on SUVs a few years ago, only Fords rolled. In addition, Ford did recommend 4 psi under the tire manufacturers recommendation on some of their SUVs.

Although, I have to say the primary cause of most of the rollovers, were a combination of under-inflated tires, overloaded vehicles, and hot climtates. Most (not all) happened in the southern states on hot days, at sustained highway speeds. Majority of the vehicles were overloaded, and the tires that did not blow were underinflated, so it is easy to assume the one that was blown was also underinflated.
If people check their tire pressures as temps fluctuate, there is no problem. For those with a problem, the dealer should be able to fix if they can follow the diagnostics published by GM.
It is really a simple system, four sensors (required by law, but H3 has five), a receiver, and an idiot light (H3 also has the DIC). The DIC and idiot light are just that, dumb, so if something is wrong it has to be the BCM or a sensor(s).