It's definitely overstating things. Bad dumps are possible and were somewhat common back in the day when people were spreading ROMs via GeoCities pages and Usenet, but these days databases like No-Intro and Redump have helped make sure that they're rare - you can easily verify your ROMs against known good ones.

I'm not sure exactly what statements you're referring to, but consider if you've ever seen a [b] in a rom filename, that means it's known to be a "bad dump". Compare this to roms with [!] in their filename, which signifies a "verified good dump".

Damn. I wonder how many games I fully played through back in the day against a known "bad" dump.

EDIT: Now I'm even more confused as to why some of those "good sets" would even contain known bad dumps.

I think the Good Sets were meant to archive every single dump of every game.

Once upon a time there was a program called "GoodTools" that maintained a database of all known dumps, so you could run it against your ROMs and it could identify which ROMs were known bad. Dumb completionists then decide to collect and distribute sets containing every ROM - including the bad ones - in the GoodTools database, so-called "good sets", which besides wasting lots of bandwidth and storage space (at a time when this stuff wasn't quite so cheap!) also unfortunately helped bad dumps stick around.