The biggest reason for nitrogen on street cars (excluding track/race cars) is because compressed air has moisture which increases the chance of rotting on the inside surface of the tire and wheel.
The biggest issue with high humidity in the tire is that moisture laden air has a much higher rate of expansion than dry nitrogen. Dry air will work almost as well as dry nitrogen. The problem is that many compressors are poorly maintained and will fill your tires with too much moisture.
This is another factor that could cause a false TPMS alert. Say one of your tires was topped up with a compressor that had condensed water in the fill hose and the other tires have relatively dry air. When the vehicle is driven the moisture laden tire will increase in pressure substantially more than the tires filled with dry air and cause a TPMS alert.
Sometimes it's necessary to put on a thinking cap to figure out what your car is telling you.