A false positive costs them nothing but the fees on a single transaction. A false negative costs the entire value of the transaction plus legal and administrative costs.
And possibly their merchant account if there are enough of those.
Chargebacks are very costly, and it isn't all that high a false positive rate at all given what they are doing (processing payments). In fact some of their competitors would be very happy with that rate.
Reputation. Have you not seen that post that pops up every three months or so about how some startup had their funds "stolen" (whether true or not) by Stripe?
I would have thought, those are the result of false positives, i.e. when fraud is "detected" where there (at least allegedly) is none.
I would be very careful interpreting those stories without having more than just one side.
The post is about a project called Radar. Do you believe this is what is responsible for those complaints?