It's a mathematical equation. The SAE (Society of Automotive Engineers) have done a lot of work to figure it out I assume. SAE hp is a reference calculation. All things being equal. Made for auto manufacturers. The formula corrects everything about the air that effects engine output. 25 deg C temp, 29.235 in-Hg pressure and 0% relative humidity. I've never used a dyno but I imagine it corrects these values itself otherwise there would be no SAE hp.
Play with this calculator to learn more about how air effects horsepower.
Engine Tuning Calculator - using dew point
Yes, your first and last sentences are exactly what I'm talking about. It's just science. My point being that I doubt the dyno always automatically populates the exact information at the time of the test. So the operator can, or has to enter the values manually and then the numbers change.
If you look at the 170HP run, you can see temp=81.25F, press=30.05, and humidity=25%, giving an SAE # of .98, which is effectively a 1:1 of displayed power on the dyno to power output by the bike. All of these numbers seem realistic based on other dyno numbers people have posted previously.
Now look at the 206HP run. You see temp=94.89F, press=27.51, and humidity=62%. The SAE # is covered up by the 150MPH speed number on the sheet, but the math works out to roughly 1.2.
So basically, by inputing high temp, very low pressure, and high humidity, the dyno adjusted the power up from the actual output of the bike by 20%! And that's one way to get 206HP out of your Pani!
I don't know the tuner who did these runs, but it sounds like he has a good reputation. I bet there's a high probability that he was demonstrating how much environmental conditions affect HP numbers, and how you can "make" big numbers.
We have a saying in R&D Flight Test- "Only trust statistics that you personally manipulated."