That was Mike Sandford's report, not Pete's.
The below seems to suggest nitrogen, or CO2, is not going to make any difference.
https://powertank.com/pages/nitrogen-truths-and-myths
But the presence, or absence, of water vapor might make a difference. Apparently water vapor doesn't behave as an ideal gas at higher pressures. Might be worth checking with a test on a humid day.
If oxygen is permeating through the tire walls that's actually a good thing since it's reducing the pressure increase we see between pre and post-cals.