The noise distribution the analyzer shows is correct and has to do with the Rayleigh function.
(dl4raj you remembered the right thing)
I am anything else but not a mathematician, so I can not serve with a simple answer, but the internet is informational about.
google "rayleigh noise spectrum"analyzer "
An interesting article is "hp_sa_and_noise_5966-4008e_an_1303.pdf" and one of keysight, lost here in the shuffle
at the moment.
What still is not to explain is the difference of the the amount of noise shown
between our instruments. They should show not more than less of a dB difference.
We should agree on setup for comparison. Same frequency, span, attenuation, bandwidth, signal level, cables etc.
RG58 is not double shieded, and MIL is meaningless in this context.
You have not answered if we have the same firmware in our instruments.
Your noise was much higher even at the high frequency side, the cause of that has to be investigated first.
I have sent you my phone number, look at your messages, so I think we can advance the progress of solving this mystery.