What you describe is not overdraft protection, it is overdraft. The term overdraft protection applies to actions that the bank would take if you are in a situation which would otherwise result in overdraft, like making a transfer from another account or credit, or declining a transaction.
As the banker has explained to you, overdraft protection is not offered in that bank. It is not required to be offered, but if it is - it cannot be forced. I.e.: the bank cannot transfer something from another account under your name to cover the overdraft (some banks used to do that), or charge your credit card, which would lead to cash-advance fees and interests (which some banks also used to do) without your prior approval and permission.
But in this case they're not offering you that option at all. If you end up with an overdraft you'll... end up with an overdraft.
The responsibility to avoid overdraft is yours, not theirs. They're not obligated to bounce your checks or refuse your payment orders because of insufficient balance, but they're also not forbidden from doing that. They can charge you a fee for either allowing overdraft or refusing a payment because of insufficient funds (or both). You should also remember that if your check bounces because of insufficient funds, it may be treated as a "bad check", and writing bad checks is usually a crime. What the banker told you is that they cannot guarantee that they will always bounce bad checks or refuse payments, but it doesn't mean that they never will.
TL;DR: the bank is not doing anything wrong, and it is indeed your responsibility to avoid overdrafts. They are not legally obligated to offer you overdraft protection.
As pointed out in the comments, the bank cannot charge you NSF fees for debit card transactions without your opt-in (I.e.: debit card purchases or ATM withdrawals). But it can for any other transaction. Even without charging a fee, the bank can allow you to go into overdraft via a debit card purchase and then charge NSF fees on the subsequent non-debit transactions.
See Rule 1005.17(b) here:
(b) Opt-in requirement.
(1) General. Except as provided under paragraph (c) of this section, a financial institution holding a consumer's account shall not assess a fee or charge on a consumer's account for paying an ATM or one-time debit card transaction pursuant to the institution's overdraft service, unless the institution...
The rule also says:
(2) Conditioning payment of other overdrafts on consumer's affirmative consent. A financial institution shall not:
(i) Condition the payment of any overdrafts for checks, ACH transactions, and other types of transactions on the consumer affirmatively consenting to the institution's payment of ATM and one-time debit card transactions pursuant to the institution's overdraft service; or
(ii) Decline to pay checks, ACH transactions, and other types of transactions that overdraw the consumer's account because the consumer has not affirmatively consented to the institution's overdraft service for ATM and one-time debit card transactions.
Which means that other transaction types are explicitly decoupled from the debit card opt-in requirement.