That assumes, of course, that the underlying paying customer is even aware how the network is luring its clicks.

Correct. While we do use Facebooks tracking for ads placed on Facebook, traffic from all other source is piped through a partner that does referral tracking and ensure that we aren't paying out commission to more than one referrer per sale. I easily imaging someone wanting to funnelling everything through one advertising/tracking partner for simplicity.

Facebook needs to ensure that their setup works in a way that the rest of the business expects. What Facebook seems to lack is the resources and dedication of Google to find the fraudulent ads.