While pursuing an engine warranty repair, I was able to add in this TSB to resolve exactly the same set of problems: low-battery condition caused crazy computer reboots, unpredictable behavior, and then (after changing the battery), the TPMS and key fobs eventually--not suddenly--stopped working. The module was so confused that it didn't even register TPMS as an option in the GM DIC choices despite the fuse showing a completed circuit from power distribution.
This sort of module "wake up" requires at least a Tech2 device to survey, though the dealer I went to mentioned having used a direct serial connection after initial problems getting the module to work. Though they never referred to it as such, all these features and more are handled by the OnStar box. The flash update was also applied.
As for "free", I agree it should be since this is a corrective measure against a programming flaw and I'm out just under $100 for the diagnostics/flash work that the dealer performed. Since it's not the sort of thing GM will reimburse them for, I'm okay having paid and knowing that my car's better protected from such problems in the future. I think in the end they mildly undercharged me for such a shop service, perhaps because I was able to tie it so solidly to the TSB.