Not always a math bug. Sometimes a human bug. Tzdata can have errors (it's crowdsourced after all) that cause past UTC stamps to be incorrect because that incorrect tzdata was used at conversion time. And since most people aren't storing the tzdata version they're using with the stamp, it would be very difficult to make corrections without also corrupting other stamps.

The bottom line is, if wall time is important, past or present, wall time needs to be stored.

The only thing that can be guaranteed about a UTC timestamp is it's a UTC timestamp.

"UTC or otherwise" is important. Are you storing otherwise, or are you storing UTC? There are times where storing otherwise will lead to data loss in case the law changes whereas storing UTC would work (when you care about a literal point in time, like access logs). And there are times where storing UTC will lead to data loss in case the law changes whereas storing otherwise would work (when you care about wall clock time, like punch-in times).