I believe I mentioned ISOs that are Payfacs. Some ISOs want to act like processors, if they do, then they assume the risk. Some ISOs have their own underwritten, most banks are too conservative and will lose your business by being too cautious, you can underwrite yourself if you are big enough. I work in this domain ;) and have interacted with the plumbing from onboarding all the way to account closure.
You've confused me as well. An ISO is sort of definitionally not the merchant underwriter ("Independent Sales Organization"). Maybe you're saying some underwriters/processors who sell direct? What is an example of an ISO that is a PayFac? There aren't many players in the business so naming names might help the general understanding.