On another note, I would love to see how the company will not accept BoA issued credit cards.
Simple, don't process the credit card BINs that are BoA.
Amex BIN from BOA
VISA BINs from BoA (and purchased banks)
426428 to 29 - Bank of America (formerly MBNA) Platinum Visa Credit Card
426451 to 52, 65 - Bank of America (formerly MBNA) Platinum Visa Credit Card
430536, 44, 46, 50, 94 - Bank of America (formerly Fleet) Visa Credit Card
431301 to 05, 07, 08- Bank of America (formerly MBNA) Preferred Visa & Visa Signature Credit Cards
432624 to 30 - Bank of America (formerly Fleet National Bank) Visa Check Card, Debit
4342 - Bank of America Classic Visa Credit Card
4356 - Bank of America Visa Debit Card
435680 to 90 - Bank of America, Visa, Platinum Check Card, Debit
449533 - Bank of America (USA), National Association - Classic, Debit, Visa