The Visa rule in a downloadable PDF are found at https://usa.visa.com/content/dam/VCOM/download/about-visa/visa-rules-public.pdf
Rule 220.127.116.11 Accepting Visa Products for Payment reads:
Visa Merchants displaying Visa acceptance Marks at payment locations agree to accept corresponding Visa-branded products for payment. If the customer indicates that he or she wants to pay with a Visa product, a Merchant must complete and process the Visa Transaction as defined in the Visa Rules.
Rule 18.104.22.168 Honor All Cards reads:
A Merchant must accept all Cards properly presented for payment.
This does not apply to the following, where limited acceptance is permitted:
- Merchant Outlets that deploy Contactless-only Acceptance Devices, as specified in Section 22.214.171.124, Deployment of Contactless-Only Acceptance Devices
- Merchants that accept only Mobile Push Payment Transactions. Such Merchants must accept all Mobile Push Payment Transactions (except Cash-In and Cash-Out Transactions, which the Merchant may choose to accept)
- In the AP Region (Australia), Canada Region, US Region: Certain categories of Visa products for domestically issued Cards
- In the Europe Region: A Merchant in the European Economic Area (EEA), for certain Product Categories, as specified in Section 126.96.36.199, Limited Acceptance Merchant Requirements – Europe and US Regions
A Merchant may not refuse to accept a Visa product that is properly presented for payment (for example: a Card that is foreign-issued2,3 or co-branded with the Merchant’s competitor’s Mark).
A Merchant may attempt to steer customers who initially present a Visa Card to an alternative method of payment, but may not do so in a manner that denies consumer choice.
A Merchant may also consider whether present circumstances create undue risk (for example: if the sale involves high-value electronics but the Card signature panel is not signed, and the Cardholder does not have any other identification).
Rule 188.8.131.52 Honor All Cards – US Region reads:
In the US Region: A Merchant that wishes to accept Visa Cards must accept any valid Visa Card in its category of acceptance that a Cardholder properly presents for payment. This means that the Merchant must permit the Cardholder to choose whether to pay for a transaction with that Visa Card or with some other means of payment accepted by the Merchant. The Merchant may request or encourage a Cardholder to use a means of payment other than a Visa Card.
Visa has at https://usa.visa.com/support/consumer/visa-rules.html a link to the above rules, as well as links to forms for reporting problems, and a customer FAQ. Note that the rules are part of a contract between Visa and merchants who have agreed to accept Visa cards (and issuing banks). Customers are not parties to these rules, and probably cannot file suits based on violations of these rules.
The question also asks:
Is it legal to bait-and-switch someone as they did above? Agree to extend credit, have the person use that credit, and then suddenly decline to accept the only payment method that you know they actually have available to them to settle the debt they've incurred with you?
Anyone who has a visa card must also have a bank account used to pay charges on that card. Or if such a person has no bank account, then any method used to pay the credit card could be used to pay the creditor directly. A person could simply write and mail checks on a bank account account to the creditor. (And while the creditor might be able to refuse chase direct transfers, they cannot refuse valid checks under the UCC.) A person could purchase and mail US postal money orders. A person could also, at many banks, arrange for direct debits or e-checks from the bank account to the creditor. Unless the contract between the merchant and the customer specifically agreed that the merchant would accept Visa payments, it has no obligation to continue accepting such payments.
So it is simply not the case that a person has no other method of payment available.