I did a trek in 2007 & 2008. I did a cavalcade in 2010. Each time, I only had to show that I had a first aid kit. It wasn't inspected.
We suggested to our crews that they each carry a few bandages & blister care in a small ziplok baggie. That supplemented our main kit carried by leader w/ Wilderness First Aid training. In my experience in the Philmont backcountry, you have a lot of minor problems - blisters, upset stomach, etc - or you need a medivac. The minor problems are annoying. The medivac episode we had (heat exhaustion/unconscious Scout) really scared us. Since that 2008 medivac episode, we haven't been on a High Adventure trip that we didn't also have a SPOT emergency beacon with us (09 Northern Tier, 10 Cavalcade, 11 Sea Base, our planned 2012 Northern Tier trek, and three Grand Canyon & Big Bend backpack trips).