Sure they can. A low false positive rate is almost a given. Low false positive rates are acceptable everywhere else, even in medicine, and when the "cost" is a minor inconvenience for perhaps millions in time/energy saved, its an acceptable business choice, even for me as a consumer.

(You note that Stripe has no business with the consumer. Well, then, this doesn't affect your relationship with Stripe, because there is none. It affects your relationship with your card's fraud prevention, which has and will always be there...)