As Shadorne says, moving the meter even a fraction of an inch can cause large changes in higher frequencies especially when comb filtering is present. Just move you head side to side over the meter at 2000 hz and if it is present, you will hear it easily.
Even if you didn't move the measurement position at all, the location of your body can change the measurements dramatically at higher frequencies. As you move around the meter, you shield the meter from some direct reflections and/or cause new reflections towards the meter. Try it and see.
Does the Rives disk use warble tones? These help to minimize these effects.
I have come to use the RS meter only under 200 hz and use a Behringer for viewing the entire FFT spread spectrum. The ramdon frequency pink noise tends to "average" over the response and allow you to see how flat it is without seeing all of the upper frequency peaks and valleys which will always be there.