Probably not legal advice. More likely any answer to your question could lead into an explanation of tax consequences, which tend to depend on specifics of your tax situation.
Giving tax advice in itself cannot violate a law the way unlicensed dispensation of legal advice can. However, one can in theory incur liability for improper tax advice. Also, CPAs and individuals qualified to prepare tax returns are subject to IRS rules on giving tax advice.
Anyone can provide legal and tax information (as opposed to advice), but those who are close to professionals that can be sanctioned or sued for malpractice tend to err on the side of not doing so outside of a proper client relationship.
So back to your original question: A bank can (and I would argue should) communicate the general consequences of linking a SSN to an account. (In fact, it's not hard to imagine the FTC, OCC, or some other regulator at some point requiring them to disclose how they use your SSN.)