At least one layer of human support needs to have the ability -- not just the ability, but the obligation! -- to escalate to your team when a customer service problem occurs that doesn't fit a pattern of known/active scams and they are unable to help the customer themselves. Sounds like that's not currently the case.
In these cases, it's also really important that customer support stick to a script and can't be abused as part of social engineering, hijacking, or fraud check bypass. "No we can't reset your account" is a very important protection too. I agree that there is an obligation to escalation, but I suspect the focus of the COE will be on how we could have detected this without human judgement. There's got to be a way.
One obvious approach would be to charge for access to human support. I'll bet the OP would happily have paid $50 to talk to someone with both the ability and inclination to escalate the issue. In rare instances such as this one where the problem really is on your end, the $50 would be refunded.