At our Credit Union we request ID if we do not know you and I generally request the staff to allow me to ask what we have done wrong to lose business so we can improve as an organization.
I can't speak for other FIs, but I know we have the capability to electronically store your signature so when you're doing a transaction we can verify it. HSBC may have something similar.
Joint accounts are generally setup one to sign, so it doesn't surprise me only one person was required to sign the account closed. There is no difference between you closing the account tand you both having a debit card and one person draining the account.
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