> "what would be the rationale or incentive for a private payment processor (in a competitive payments market) to reject a legitimate transaction?"

Paypal cite the following reasons that they may freeze or suspend an account (at their sole discretion):

    - You’ve received an abnormally large amount of money in your account that is way above your average
    - Someone has filed a complaint to Paypal about your business
    - A series of chargebacks have been placed against your account
    - Your website has questionable content
    - You are in violation of Paypal’s use policy. For example if you sell drugs or anything illegal, you may get banned
    - Your account information is not up to date or your account is not fully verified
    - Someone has logged into your Paypal account from a strange location.
    - Your credit score is low or something with your background history makes you a higher risk customer
    - They have detected fraudulent activity on your account.

Some of these are reasonable. Some of them are highly questionable. Some of them are outrageously open to abuse.