You missed my point. Yes, it's a claim and the investigation has to begin. I didn't say otherwise.
The claim being investigated is whether the transfer was unauthorized. There are two consumers on the account and they each have a card. If the transfer was initiated or authorized by either of them or either of them benefitted from it, then it's not unauthorized.
If Joe says the transaction was unauthorized, it's relevant that the transaction was done with Jane's card because the bank will want to find out whether Jane did the transaction. If they've got ATM video showing her doing the transaction, they can deny the claim in spite of the fact that Joe says it's unauthorized.
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Nobody's perfect, not even a perfect stranger.