I agree, but it's not clear if the situation was "hey we paid, look at our docs" and hetzner was just like "no give us money" and they were like "no we're not paying", or if hetzner just shut them down without recourse.

Personally, if I knew they were gonna shut me down if I didn't pay before X date, I'd fight it up until X-2 days, pay it, then continue fighting (depends on the amount of). But it's not clear that OP was given such a deadline.