Actually Boltzmann doesn't apply to a thermionic voltage regulator. It's not a resistor and the conduction process is totally different, hence the higher noise. If you think that's high, have a look at a 20V Zener diode passing 50nA. Noise is in the order of 200mVpp. But again, that's avalanche noise not Nyquist thermal noise.
Hmm, there's a thought :