While I agree you have the right to use any lounge as you wish, I somewhat see MH’s logic though - you’re entitled to use the lounge prior to your departure. Not arrival, as MH doesn’t have arrival lounges.

So in your case you’re departing to a domestic destination, which leaves from a separate area that requires you to first clear immigration when you arrive internationally. As your entry to the regional (or satellite, for the matter) lounge hasn’t yet “cleared immigration”, you technically haven’t been cleared to fly domestically - possibly a technicality that has been drilled into the lounge attendants.

That said, I’ve spent long hours at the satellite J and F lounges after arriving internationally and en route to a domestic flight. So this rule is somewhat YMMV. I personally don’t see the wrong in letting people choose which lounge to go to, provided you have sufficient time and plan to clear arrival immigration and arrive at your domestic departure gate on time.

FWIW, the regional and domestic lounges are comparable generally - same decor and furniture, same food and beverages.