Ah, I didn't know that. Where did you find this information about "digital grounding"?
Perhaps that helps to explain how the scope is able to calculate and display a large RMS voltage measurement value even though the channel input is "ground coupled" and the display is showing a flat line at 0V.
Somehow this "feature" of the DS1000z series leaves me rather cold.
Okay, I re-checked that again and I seem to be somewhat in error here
-- the situation is a little more complex:
The analog front end of the DS1000Z series hasn't got a proper grounding switch/relay, the input stays connected to whatever source it is attached to (see Dave's reverse engineering thread:
https://www.eevblog.com/forum/blog/eevblog-675-how-to-reverse-engineer-a-rigol-ds1054z/). Yet, there's still some noise displayed when sensitivity is wound up to maximum and input "grounded" via the vertical menu function. This noise is much less than with an "open" or externally terminated input. A closer look at the ADC that's presumably used in the instrument (Hittite HMCAD1511) shows that most of the attenuation/amplification is done with the (so-called) "digital gain control" which permits a 1:50 digital gain range (1:32 without missing codes) -- this matches very well with the 1:50 "hardware" attenuator in the front end (the relay you hear clicking between the 200mV/500mV (1x) range). There's one more section in the ADC that is relevant here and that's the input cross point switch (MUX Array). This is used to harness the four 250MSps channel inputs in the ADC to form four individual 250MSps, two 500MSps or one 1GSps channel(s).
It's not particularly mentioned but looking at the input matrix switching scheme
http://www.analog.com/media/en/technical-documentation/data-sheets/hmcad1511.pdf, it should be possible to run the ADC with all the analog inputs disconnected which is in my opinion exactly what Rigol does to "emulate" a grounded input. The digital gain is still active but there's no connection between the ADC and the preamplifier. Hence, all internal noise generated or picked up by the analog input circuitry, will be camouflaged. The residual noise is just ADC and ADC interleaving noise (switch between single/multiple channels while observing a "grounded" input at maximum gain and 5ns timebase resolution to observe this).
To cut a long story short, the result is basically the same - you won't be able to tell if the analog front end amplifier is picking up the noise internally by setting input connection to "Ground".
Cheers,
Thomas
P.S: congratulations on spotting the source of the noise! It's quite amazing what crap some "el cheapo" power supplies are...