I did a same-day turnaround in LAX about two years ago. It wasn't a MR... I was going out to meet my then-boyfriend (now husband), who was flying home SYD-LAX-DFW after a month in Australia. I did not exit security; I simply went up to the GA for my flight and asked to check in. He gave me some funny looks ("Where did you come from?" "Dallas." "Where are you going?" "Dallas.") but he was able to do it.

If you get any flack, and you don't feel like explaining the MR thing, just say you were coming in for a meeting at the AC.