Does nitrogen pressure in tyres fluctuate to much a lower degree than air with changes in temperature?
There can be no scientific explanation, because the argument itself is incorrect.

For the most part air is nitrogen.  To be specific, about 80% of dry air is made up from nitrogen.  In fact both nitrogen and oxygen, the second major components of air that takes up almost all the other 20%, behave extremely like ideal gas.   Pressures of dry air and pure nitrogen gas at different temperatures, from far below freezing point to above boiling point, have indeed been measured to incredibly high accuracy.  The difference between these two gases is below 0.1%.   In fact, near room temperature, many types of gas are close to ideal gas and have very similar temperature profiles.

I am not sure why people are comparing nitrogen with water in that question thread you mentioned.  Water is a minor component of air and its concentration varies so dramatically across places.  However, even in a summer day, at the maximum humidity of 100%, the amount of water in the air is only 10% of that of oxygen.

Basically, pressure of nitrogen gas do not fluctuate less with change of temperature compared to normal air.