Maybe I'm missing something.
I don't think you are missing anything, David. I have seen this argument from lenders before as they (possibly unintentionally) don't want to acknowledge that they took adverse action.
For example, I saw a bank that had a procedure to call refinance customers up when their appraisal came in low and ask them how they wanted to proceed (as there were many hypothetical options for proceeding, as the OP's mortgage team pointed out). 99% of the time, the customer would say to forget it, and the bank would ask for that in writing, getting the "expressly withdrawn" documentation so they could avoid an adverse action notice under Reg B and report this as "withdrawn" for (old) HMDA. When the examiners discovered this, they cited the bank for both Reg B violations (for not sending adverse action notices) as well as Reg C violations for incorrectly coding the applications as withdrawn, when they were, in fact, denials.
BAY: For this reason, I would advocate for a combined denial/counter offer form. It makes things much cleaner in the long run and it sounds like you have a mess on your hands.