The RTA shows you the level of your test tone and the levels of harmonics at the measurement position. What it doesn't show is what the level of a test tone at the harmonic frequencies would be. The levels of the harmonics are effected by both the amount of distortion and the response at the measurement position - for example, suppose your mic happened to be sat at a perfect null for 2 kHz. A test tone at 1 kHz would show no 2nd harmonic distortion, regardless of the actual level of 2nd harmonic distortion produced. In-room responses are not flat, so all harmonic levels are effected. For more on that read Temme's paper, you may find a copy online. For more general information on distortion measurement this old B&K application note is good, though it predates sweep measurements.
When I made the last distortion measurement with RTA I was moving mic in a same MMM manner when I was making frequency response measurement. That way, the chances that mic is sitting in a perfect null for 2kHz (and any other tone) are zero, but with single sweep it can certainly happen. For that reason I am expecting RTA distortion measurement when done with MMM much more precise than when done with a single sweep. What is your opinion on that?