You're almost there.
When you sit on the bike, you would agree that the tyre compresses?
Therefore, under that compression, the diameter of the wheel is smaller - yeah?
Right - the (true) circumference is the diameter multiplied by pi - correct?
Measure the radius under load, (axle centre to ground) and multiply by 2pi.
Or the exact same thing is to sit on the bike and roll forward one turn with your full weight on the bike.
If you still can't get your head around it, do the tests that I suggested, with a couple of different tyre pressures and you'll see what I mean.
I could spend another hour typing trying to explain this or you could spend 10 minutes testing.
... Steve