You're close, but not exactly on point here. When you sign up for a credit card, you agree that the credit card company can amend the terms of the credit card agreement at any time, with X days notice (usually 15 days). Therefore, as a matter of contract law, all BOA has to do to get your assent (or "meeting of the minds") regarding the new contract term is to notify you of their intent to make the change (increase the minimum finance charge), and once notified, if you continue to use the card after the notice period has expired, your continued use of the card, by itself, is sufficient to indicate your assent to the new terms. There is abundant case law on this point, that your actions alone can express your assent to contract terms. Thus, BOA is not required to give you the option to opt out in writing order to get your assent to the new terms.
The reason why BOA gives its customers the option to opt out of the new minimum finance term by giving notice in writing, is to set up a defense to the argument that the new term is unconscionable. If they did not provide that option, an arbitrator might conclude that although the cardholder assented to the new term by their continued use of the card after notice, the cardholder really had no realistic choice if they wanted to continue to use the card, and therefore, the term was unconscionable and unenforceable. (In laymans terms, the new term was presented on a "take it or leave it" basis, with no real opportunity to bargain) They would then be facing a class action lawsuit on behalf of all of their cardholders. However, by offering a choice to reject in writing, BOA will argue that the new term was not unconscionable because the cardholder really did have a choice...he could have simply declined by giving written notice, and the new term would not have taken effect. If this argument prevails (and it might), then they would be able to succesfully defend a class action suit (or, more likely, it would not be brought in the first place) Of course, BOA knows full well that the vast majority of its cardholders simply don't read the fine print of every change to the cardholder's agreement, and even those that do probably won't care enough to write. And they probably know that the people who are diligent enough to actually read the fine print are the same people who are diligent enough to pay the bill in full, and they don't have to worry about finance charges in the first place. Therefore, BOA knows that only a tiny percentage of people will opt out, while the vast majority of people who pay finance charges will be charged the higher fee, and they have (arguably) innoculated themselves from an unconscionability challenge and an expensive class action suit.
