I was told that a pair of Red Wing Irish Setter boots won't work for going to Philmont Scout Ranch, because they've never seen them (according to Philmont outfitter boots department). I'll be doing Itinerary 6 as an adult leader. This is a 66mile route over 12 days with approx 10000 ft total height gain.
I haven't seen any particular rules for boots at Philmont. I am aware of a wide range of footwear having been used, ranging from the traditional heavy high-topped boots to lightweight, low-cut trail runners.
In general it seems the Philmont trails are well-maintained, and with the exceptions of places like Valle Vidal (off-trail) and Mt. Baldy (plenty of scree) the terrain should not pose any problems that demand specific footwear.
This means you can fall back to the basic rules of hiking footwear: that which fits properly, does not hurt your feet, and does not cause blisters. If you have used your boots before, and have had no issues with them, I would recommend sticking with them.
On the other hand, if you are buying new boots and gear for Philmont and are lacking backpacking experience, you will want to spend a few hours trying on different brands of boots and walking around in them in the store. Once a comfortable pair is found, you will then want to do a number of practice hikes.
Another question will be the weight of your gear; most people wearing trail runners will likely also have reasonable pack weights (e.g. 20-30 lbs or 9-14 kg). Knowing Scouts, the packs may lean toward horrendously heavy, and that's an argument for boots with decent ankle support.
A similar question was asked on BPL a few years back, so I suggest reading over the responses to that as well: http://www.backpackinglight.com/cgi-bin/backpackinglight/forums/thread_display.html?forum_thread_id=41005
These boots seem perfectly reasonable to me. If they are comfortable and not about to fall apart I can't see why they should be a problem.
I suspect what they mean is that the are not familiar/do not stock that brand of boot so can't recommend it. It would seem crazy to me if they said you can't use perfectly good boots because they aren't on some list.
If you are mainly on good paths then the comfort of your boots is probably the biggest concern.
Also, if you've had the boots for a while make sure they are in good condition and will not fall apart half way through, as that is bad!