There are many sub-claims in the question. I'll focus on only one of them - air loss, compared to nitrogen loss.
This article (Nitrogen loss study) suggests that while nitrogen filled tires did lose a bit less than air filled tires, the difference is not terribly large.
The fact is, air is roughly 78% nitrogen. (I don't think this statement needs any research to back it up.) The remainder of air is mainly oxygen, a bit of CO2, some water vapor, some methane from the cow down the road or the beans I ate for dinner, etc.
The point is, if nitrogen moves so slowly compared to "air" which is mostly nitrogen, then the air inside the tire would quickly become strongly nitrogen enriched, because only the oxygen and other gases leave. Then every time you add air to fill the tire again, the volume inside becomes more and more strongly nitrogen enriched, quickly becoming nearly pure nitrogen after only a few re-fills.
The study I cite in fact suggests that some of this is happening. They state that a 30 psi air filled tire lost on average 3.5 psi, versus 2.2 psi for the nitrogen filled tire. That is, an air filled tire lost 3.5/30 = 11.7% in volume. In that study, a nitrogen filled tire lost 2/30 = 6.7% in volume. This suggests the additional 5% loss in volume must have been almost entirely oxygen. If this is true, then in fact the oxygen is indeed migrating out at a rate that is several times faster than the nitrogen.
The obvious conclusion is that the other stuff that comprises air must be migrating out at a preferentially faster rate. (Unless someone can postulate a mechanism which would enable the oxygen in air to mitigate faster movement of nitrogen too.) The preferentially faster loss of oxygen in the tire would be easily testable. In fact, one could not actually breath the air from inside a tire if it was that significantly oxygen depleted. As I said, this would be easily testable, although I don't know of any tests having been made. In fact, while it is purely anecdotal, I have heard of people inhaling the air from inside a tire, and not quickly succumbing from the lack of oxygen. This suggests a problem with the logic above. Only a test and experimental evidence can resolve the question.
Edit: Some simple algebra suggests that for air to have the greater loss as described in the study, if this is because oxygen is escaping at a faster rate, then the loss rate for oxygen (and argon, etc.) must be 29.4. Thus over a set period of time, 6.7% of the nitrogen will escape, but 29.4% of the oxygen will escape in that same period of time. That extent of oxygen depletion would be easily measured. If this is true of course, then the claim that nitrogen will migrate 3-4 times faster than air is false. While it MAY migrate roughly 4 times faster than pure oxygen, air is not pure oxygen.
Thus, if we are to believe the study (and the conclusions I've drawn from it) then the claim about the loss from a pure nitrogen filled tire has been falsely inflated, as if air was composed of pure oxygen. An inflated claim, strangely like the inflation of a tire. Does this invalidate the other claims? It should cause you to wonder if the other claims were also inflated by a bit, since if one is willing to play with the numbers once, they will surely be willing to do so in other respects.
Re-edit: In an effort to beat this horse completely to death, suppose that a pure nitrogen filled tire did deflate at a rate 3-4 times slower than an air filled tire? What would this imply about the exfiltration rate of the non-nitrogenous components of air? Again, a bit of arithmetic yields the answer. If it is 3x slower, then we have oxygen depleting at a rate of 67.6%, compared to the 6.7% for pure nitrogen over the same period of time. If the difference is 4x, then we would have 98% of the oxygen lost in the same time that 6.7% of the nitrogen migrates out.
Look at this over the long term. Suppose we allow our tire to deflate by 10%, so from 30-27 psi, and then re-inflate it with simple air from the pump. Since most of that air is nitrogen, it is replacing the oxygen we have lost. Clearly this will take only a few cycles before we approach a steady state. That steady state composition of the air in our tire will be approximately 98% nitrogen, and 2% oxygen. So nearly pure nitrogen. Again, the point is, why bother to inflate our tires with pure nitrogen when the simple act of inflation and then re-inflation to replace what is lost will yield essentially pure nitrogen anyway?
