Your situation is identical to that of the original poster except her query was verbal and yours is in writing. If it is not a summons, then the IRS employee advised you correctly, you are not obligated to respond. I cannot imagine that a bank would want to respond voluntarily.
One of my previous employers simply forwarded the IRS letter to the customer on the assumption that there might be a reason the customer would want to contact the IRS. It was accompanied by a two sentence cover letter saying the query had been received, but it was bank policy not to divulge customer information unless it was compelled or authorized by the customer to do so. This was years before the GLB disclosure, but it would still seem to be a workable response.
In this world you must be oh so smart or oh so pleasant. Well, for years I was smart. I recommend pleasant.