First of all, welcome to the BOL forums!
If I'm reading your post correctly, I agree with you and raitchjay and NOT with your regulators. The cash-out (reported as cash-out refinance) vs not cash out (reported as a refinance) only comes into play once you determine that you have a refinance. In other words, there are two types of refinancings for HMDA: cash-out and not cash out (reported as a refinance). So, if you don't have a refinance by definition in 1003.2, you would not report the application/loan as either a refinance or cash-out refinance. It would have to be a purchase, home improvement, or other purpose.
(p) Refinancing means a closed-end mortgage loan or an open-end line of credit in which a new, dwelling-secured debt obligation satisfies and replaces an existing, dwelling-secured debt obligation by the same borrower.
I would absolutely push this up the chain of command. Otherwise, you will have a mess later if you now try to comply with what they told you, because what they told you is wrong.
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Adam Witmer, CRCM
All statements are my opinion, not those of my employer, and should not be taken as legal advice.
www.compliancecohort.com