When Reg E was modified to allow truncation of account numbers on receipts it was done for privacy/security reasons. There was no conscious effort to make the same allowance on statements, however. So Reg E 1005.9(b)(2) requires the account number. But if you go to the EFTA itself 15 USC 1693d, the law does not list the account number as a requirement. The fact that the law trumps the reg might be arguable in this case (but weak for this), that fact that as Brian explained a truncation still allows positive ID, and the account number is not required to file a claim, it is debatable that the entire account number is required, especially as the bank balances the risks of information security and accomplishing the intent of Reg E.
I do not believe the statement account number was intended to be truncated. It's one thing to leave an ATM receipt on the ground, but statements should be protected by encryption and passwords or an envelope and postal law protections. I also do not believe it impedes the consumer in any way, though if any bank does demand the entire account number it may be at fault if account opening was the only time it was provided. If I had to choose the letter of the reg (not the law in this case) I'd say it should be provided. But again, it isn't necessary for most applications. I suppose if I was setting up direct deposit and needed it, and I was in a far away time zone, I could legitimately complain if I had no access to that number. But 99.9% of the time the truncated risk favors the consumer and the bank. Hopefully an examiner won't raise the issue.
The succinct answer to the original question is, IMHO, NO, the account number is not needed to file a claim under 1005.11. It says a requirement of a claim is information which "(ii) Enables the institution to identify the consumer's name and account number; ..." When I teach Reg E I use as an example filing a claim with my name and "my checking account". If I have one DDA, I'll bet dollars to donuts you don't have but one Andrew M Zavoina and that identifies what is required.
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AndyZ CRCM
My opinions are not necessarily my employers.
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