First, regarding the substantive issue: It doesn't matter whether the amount is received as a statement credit or as a deposit to a bank account. See Rev Rul 76-96, where it was held that a rebate is not included in income even though paid as a separate cash payment. I've attached a PDF of that ruling because I can't find a free version online. That ruling was later suspended in part, but the later suspensions are not relevant to the issue under discussion here so we don't need to go into that.
Note that I am not saying that the credit card reward is nontaxable. I am just saying that whether it is taxable or not is not going to depend on whether it was received as a statement credit or not. The form of payment just doesn't matter here.
As for whether the reward is nontaxable, the IRS has accepted in a private letter ruling,
PLR-141607-09, that a 1% credit card reward constituted an adjustment to the purchase price of the item and was therefore nontaxable. Unfortunately, private letter rulings are not precedent and cannot be relied on by other taxpayers.
26 USC § 6110(k)(3). The private letter ruling gives a hint as to how the IRS
might view your case, but it is important to understand that the IRS is generally not bound by its dealings with other taxpayers, and it might come to a different decision in your case even if the situation is completely identical. See
United States v. Mendoza,
464 US 154, 161 (1984) (noting that the US government is free to take different positions in cases involving different parties even if the issues are identical).
I express no view on the ultimate issue of whether the amount is taxable.
As for any potential Form 1099: It basically doesn't matter what the Form 1099 says. The taxability of the amount is determined by applying the law, not by reading a Form 1099. That said, if you receive a Form 1099 and you disagree with what is stated on it, you can write a letter to Bank of America and ask them to change it, but you are not required to take this step. You also have the option of suing Bank of America under
26 USC § 7434(a) if you believe that they "willfully file[d] a fraudulent" Form 1099, but again, you are not required to take this step and it is not relevant to whether you owe the tax. I express no view on whether such a lawsuit is merited or whether it would be successful.
If you determine that the amount is nontaxable but is included in the Form 1099 anyway, you are not bound by the Form 1099, and you can just take the position on your return that the amount is nontaxable by not including it in your income. Again, I stress that I am not commenting on whether the amount is nontaxable, but if it is nontaxable, you don't have to include it in your income, even if it is included on a Form 1099.
If you file a paper tax return, you can attach a written statement explaining why you are not including an amount that was included in the Form 1099. If you do this, the IRS might not ever contact you about the discrepancy and might just accept your explanation. On the other hand, they might disagree. We can't predict which will happen, and I offer no view on that.