No, No. You completely misunderstood me. My fault I'm sure. My point was that the picture we get of these mBH's is like they're this tiny asteroid lost in a vast solar system where they are surrounded by stately moving giants. Sure collisions happen, but not very often. But if the planets were not bound by the speed of light and Newton's laws and instead moved chaotically many times the speed of light, then the collision rate would go up. This is sort of like the situation an mBH faces when inside the center of the Earth, except that nothing moves relativistically. I was just trying to create a visual explanation. Forget I said it.

As for your velocity calculation, I think k_B should be 1.38 x 10^-23 J K^-1. Also I think you also may have forgot to take the square root. I recalculated the mean speed, and got a value of 1.7 km s^-1 (see footnote 16, I had to multiply by 3^1/2 to get the right speed--only a factor of 3/2 difference from my first estimate, which means I was in the right order of magnitude ball park. So my conclusions still stand. I think.

Tomorrow, I'll try and calculate the minimum effective speed below which evaporation dominates accretion.