Hey Cindy,
Perhaps a bit late, but I agree. I do not see an "out" from the requirement to provide a periodic statement in this situation. It is not mentioned in any of the exceptions under 12 CFR 1005.9(c). As long as the EFT happened within the monthly "cycle," whether the last day or not, then a periodic statement would be required.
[(b) Periodic statements. For an account to or from which electronic fund transfers can be made, a financial institution shall send a periodic statement for each monthly cycle in which an electronic fund transfer has occurred; and shall send a periodic statement at least quarterly if no transfer has occurred. The statement shall set forth the following information, as applicable . . .]
[1. Periodic cycles. Periodic statements may be sent on a cycle that is shorter than monthly. The statements must correspond to periodic cycles that are reasonably equal, that is, do not vary by more than four days from the regular cycle. The requirement of reasonably equal cycles does not apply when an institution changes cycles for operational or other reasons, such as to establish a new statement day or date.]