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Here's some basic physics about the nature of noise.

Thermal noise power can be measured using noise power = kTB .

T = temperature = Kelvin = 290K at room temperature

k = Boltzmann's constant = 1.38 E-23 J/K

B = Noise Bandwidth (Hz)

So if you change the detection bandwidth B by a factor of 10 then the power at the detector will change by a factor of 10. (because you narrowed the access window that the noise can get through by a factor of 10)

So this noise power to bandwidth B relationship will equally affect both external noise signals and internally generated noise inside the analyser. BASIC PHYSICS and endorsed by Hewlett Packard since at least 1974.

The S/N ratio of the noise you are trying to measure against the noise inside the analyser will not improve/change with a change to a narrower RBW. This is because both the noise contribution from the analyser and the noise signal of interest BOTH have to pass through the same (narrower) RBW filter so they BOTH go down by the same ratio of 10dB as they BOTH get sliced into a narrower slice of noise by a factor of 10. A Slice of noise 10 times narrower will have 10 times LESS power. I hope this helps

Good luck to you if you still want to prove that modern physics has this simple concept wrong