You cannot measure noise on 1µs/div. You are high-pass filtering low frequencies out. Pretty much all of the 1/f noise which is actually large part of noise in scope amps..
Set scope at 1 ms/div, 1mv/div, and NO 20 MHz BW limiter.
To see what is actual noise with 100 MHz BW.
Then repeat with 20 MHz limit.
And if you look at your stats, you have very large difference between max and min AC RMS value.
This is the point where you reset stats and see again. If you again accumulate have such a large difference between max and min AC RMS something is wrong.
Make sure to put a non shorting cap (or wrap a piece of aluminium foil over BNC) on input so there is not induced voltage.
Shorting input with 50 Ω is not going to show what noise is with 1MΩ inputs but less, which is not what you going to see with passive probes connected.
Whenever i have shown any data from any scope that is how it's done.
50Ω measurements are separate set of data.
If you still have large excursions in AC RMS, maybe you have some popcorn noise or something.. Or EMC problem.