I also feel that technically, at least according to the source, my comment is correct.
As the piece notes:
Women could participate in the economy — including banking — in Colonial America.
To me, this meets the "American women could open a bank account" criteria but that's just my opinion and one with which reasonable people can disagree.
Though, the piece's source gets delightfully snarky about it:
Though a small percentage of all bank customers, women held accounts in many northeastern banks in the early national period, a fact that apparently has eluded business and women's historians alike.