is there any evidence to suggest that de-prioritizing food increases
Anyone who has ever prioritized food and died of any of the other issues would be evidence that de-prioritizing food would have increased survival. If someone spends a couple days setting traps, snares, and fishing lines only to realize they still don't know how to get fresh water and dies on the third day would regret not prioritizing water.
You note in your quote the emphasis is the typical scenario of being rescued in a few days. Food is barely an issue then, but all those other factors could kill you.
Don't forget to use your brain though! It is your most important tool for survival. If lost in a forest at 40 degrees latitude late spring or early autumn and the weather forecast was no rain for a few days, then tending to a shelter early on is foolish. If I expect a search dispatched within a couple days, I'm also going to ignore the "rest" criteria and spend lots of energy preparing a massive smoke signal that cannot be missed.
Don't throw your logic out the window. Just use the priority list as a reminder of what could kill you first, and remedy that if necessary.
A specific use case...
On the other hand, if you believe that there is a very real possibility that you might be stuck long term, then you need to tend to every one of the needs on that list, and you only concentrate on the higher priority ones to the extent that you need to mitigate them.
For example, if I was extremely lost very deep in the wilderness, neglected to leave any travel plans with trusted people back home, and it's early spring at about 50 to 60 degrees latitude so I do need to worry about severe environmental conditions but the weather is good at the moment, my first two actions would be to set up a covering to protect against rain/snow and to find a water source. The water search would actually come first, not because it's more important than the shelter and rest, but because I want to set up the shelter near enough to the water to assist my long term goals, so I combine shelter and water in my first action. It beats rest temporarily because I'll need to find water anyway, and "search -> water -> rest" is better than "rest -> search -> water (when already dehydrated)".
As soon as I can after shelter + water, I'm going to try to do something for food. Food beats out signals/communication right now because I don't expect anyone to be searching for me, so I expect the signals to be in vain, but I know that I need to avoid starving.
This scenario was forced on us by negligently not informing anyone of our travel plans. Remember to provide that information to at least 1 trusted individual before your travel! If I had not been so foolish in this use case, I could have prioritized signals and drastically improved my survival odds.
But since it is what it is, working on development of food sources comes before signals. But as soon as you can either break from food or multitask, then I'd work on signals. Eventually the situation might come that I can signal for help, so I do want to have that option available.
Air was never at risk in this use case.
So in this specific use case, the situation-specific order of events that I would have thought about ended up being 1) water 2) shelter 3) rest 4) food 5) signals/communication, and air is not even on the list.
That does not mean that air is not the highest priority - it is. Or that sheltering from rain and snow in that environment is not more important than water - it is more important than water. But I would have used the combination of the survival priority list with my knowledge of my unique circumstances to juggle priorities and maximize long term survival.
In fact, if you want to follow your priority list strictly, one could even put it this way: "Air? Satisfied. Shelter? I have a tent (tarp, bivy bag, whatever) so I can shield from the rain or snow quickly if needed, and weather's ok for now so satisfied. Rest? Not satisfied, so I should get a rest as soon as is reasonable. Signals? Not satisfied at all, and I was dumb so nothing I can do about that for now. Water? Almost out, not satisfied, get more as soon as possible. Food? Almost out, but it can wait since I have more pressing needs." Running through the checklist just like that and following it to a tee would get you results similar to what I said above, with the only difference being water wasn't queued up as efficiently.