That's entirely wrong. As long as neither spouse has any other, disqualifying coverage, both spouses are eligible individuals even if both are covered under the same family HDHP plan. I suggest that you (and the HSA Bank rep) read IRS Pub 969 and section 223(c)(1) of the US Code:
<a rel="nofollow" target="_blank" href="
https://www.irs.gov/pub/irs-pdf/p969.pdf">https://www.irs.gov/pub/irs-pdf/p969.pdf</a>
<a rel="nofollow" target="_blank" href="
https://www.law.cornell.edu/uscode/text/26/223#c_1">https://www.law.cornell.edu/uscode/text/26/223#c...>
