This is a simplistic question. Whether or not a company is obligated to do something depends on many things. For starters, we are not told what kind of customer (consumer, business, trust, etc.), account (demand deposit, savings deposit, time deposit, credit card, HELOC, or other type of banking service), or statement is the subject of the question. Also, we don't know where the bank and its customers reside or have any idea about the terms of service spelled out in the service agreement between the bank and the customer in question.
Making a few guesses, the answer will probably be "no," but without knowing and considering the implications of all of the factors above (and probably one or two other things that slip my mind) there is no way to get a bullet-proof answer.
Most importantly, I'll guess that the account is some kind of deposit transaction account and that it is covered by Regulation E. If so, it's probably covered by Regulation DD, too. Neither of these regulations nor the laws requiring them regulate fees. State law probably doesn't prohibit or regulate this type of fee, but that should be confirmed. If my other guesses are correct, ESIGN would be a factor--but it simply requires disclosure of the availability of replacement e-documents in paper form and the fee, if any, for this service. Finally, you are obligated to follow the terms of your service agreement (unless they violate a law or regulation.)