The average doesn't really matter. The researchers are looking for "steps" in data streamed caused by changes in the video. If you're adding random levels noise it will drown the signal that the researchers are looking for.
The random noise becomes the background and unless it is a constant addition of noise (which wouldn't save any bandwidth, might as well use uncompressed stream) you could still time changes in the signal.
The 'solution' of adding random data to hide these "steps" is a common misunderstanding of the theory behind preventing bandwidth side-channel attacks. It'll probably work in practice as long as the amount of randomness relative to the delta is sufficiently large and the attacker only can only make a limited amount of samples.
The random noise becomes the background and unless it is a constant addition of noise (which wouldn't save any bandwidth, might as well use uncompressed stream) you could still time changes in the signal.