Yeah you can dispute them but it's by no means guaranteed and it can cause further problems. You certainly would not dispute them in the case mentioned by the GP poster. So bringing up disputes is just muddying the waters.

Refusing chargebacks and not issuing refunds are two very different things with distinct language. And if you don't issue refunds for a case like the GP described, where thousands of customers were incorrectly billed, you certainly would be flooded with chargebacks and likely put your merchant account in jeopardy. (Most of the big processors would close your account if they get evidence you are fraudulently billing customers and actively resisting making it right.)

It's clearly a made up story by someone with no experience actually managing credit card payments for a real business.