Yes - and probably in response to the rocky roads up there. I found some pictures of Harper Flat (I believe they did not drive on it - but it is representative of some the rock up there). It appears to be exfoliating granite (with very little sand or dirt on big sections). A dirt road at approximately the same altitude, south of Harper Flat, would have some granite in it, IMO. It's always a worry even without the heat that such granite might damage a tire (I don't think JRF's tires look like specialized offroading tires, btw).
Heat plus granite is terrible for tires. Didn't we learn there were
three flat tires? To me that says the truck took a big bounce (or went over really treacherous rocks - which should have been visible, unless speeding). By speeding, I mean too fast for those conditions. Deflating allows the tires to be softer and avoid puncture. In heat, one deflates just because of the heat. I was taught that if the terrain is rocky, one does not deflate as much - but again, trying to account for both heat AND rocky terrain...is difficult.
Close up picture of Harper Flat rock (which underlies the whole area at an elevation of about 2000 feet and is probably also higher up):
View attachment 462093
^
Pinyon Wash/Harper Flat
This shows the grinding area of the Natives who used to live in the area and wintered there (likely grinding acorns carried up over several trips from fairly far away). But it does show the granite surface of the flat and its generally uneven character.
There are rounded granite boulders of various sizes in both Pinyon Wash and Harper Canyon, of course. But sharper ones are often embedded in roads, which is why people deflate. Most off roaders carry a simple device that can be used to reinflate, as well. I am assuming they were up there during daylight hours and would have needed to deflate for two reasons. IME, one can drive very slowly in such terrain, even with a flat tire (have done it, have seen people do it - not recommended, but possible). But 3 flat tires would really impact steering, IMO.