FWIW, arguments regarding AC(BX)/MC vs NMC in structures that are to remain 'open framing' (no wallboard) have abounded for many, many years, and varied by jurisdiction.
Looking from a practical standpoint (common sense) AC/MC can be damaged (outer jacket) between studs easier than NM. We all know that AC crimps, or 'spirals' under stress. The argument was 'storing' things (shovels, brooms, etc.) in the cavity between the studs, using the wiring that happened to be there for support of the item.
The debate may arise IF this summer home could be considered a damp location by the local AHJ. My suggestion is to speak to the local AHJ before you get into this project.
The term 'subject to physical damage' varies by interpertation!
Yes, you can damage NM, but the concensus was...not as easily.
We (NJ) had a directive (FTO)from state that NM was not approved within an open framed structure. That directive was rescinded about 3 years back. With a freesta nding resi garage, it wasn't uncommon for an owner to say the walls will be finished, and that not happening.