Take my experience with a grain of salt. No lie, I was the first male CAP Chaperone in 1998 at the New Mexico location. I did absolutely nothing special to be this at the time. I just happened to be in the line of sight of MSgt Miller(Ret), who used to be the USAF LNCO for NM wing, back when there was a such thing and he was the lead for PJOC. He was a retired PJ himself, being that Kirtland AFB is one of the pipeline school houses for the AFPJ program is one of the reasons this is held in NM. It used to be his pride and joy, cadets are deprived today not to have his special touch to the activity. My experience is probably way different than the experience now. When I did it, I was literally there because a cadet complained a year prior and national felt that they needed oversight to the oversight.
Back then, the activity was still ran by CAP-USAF, being the overall oversight with the instructors, being a meld of AF PJ's, CCT's, Army SOF types and AF SERE specialists. My ROE was that I could participate in as little or as much as I wanted, with the understanding that myself and my female counterpart were not in charge and were not to interfere with the instructor staff. We could only step in if we genuinely saw a safety violation or a direct breech of the cadet protection policy, then we were allowed to call a knock it off and express our concerns with the USAF leads and MSgt Miller. We were simply there to monitor and draft an AAR. Keep in mind this was PJOC so it was given a little more latitude on what is considered physical exercise for discipline. I believe the way around it was that a cadet being dropped was not a punishment, it was more of a motivational technique. I believe the distinction was that as long as cadet was not singled out personally, push ups and flutter kicks were allowed for screw ups. The wrong was was, "hey Cadet Snuffy, drop." The right way was "cadets drop!"
When I did it I participated in everything the cadets did except the "motivational PT." My counterpart only monitored.
Now it no longer has any CAP-USAF RAPO's involved. They pulled our funding for all national activities when I became a RAPO in 2012. It is all ran by CAP members except the instructors are still the AD and Reserve SOF types. Also my understanding at least for the NM version, is that it is no longer solely takes place at the Terrero camp site in the Pecos Mountain, due fire concerns. NM is pretty much a tumbleweed that catches on fire at a moments notice. My thought is that you probably need to be fit enough to handle a four or five hour hike in the woods during the land nav training, if they even do that anymore. When I was a RAPO I observed a small portion of it when part of it was held on base. From my vantage point, it seemed like the only active engaged SM was the activity lead, who I believe stepped away from the role after doing it for several years in 2015. The other SM's were doing standard SM stuff, like herding cats at cadet activities.