I'd like to add my input.
VBW is not the same as averaging. RBW, VBW, and sweep speed, are all related. As the video showed (great video BTW), RBW allows separation of closely spaced signals. There is a relationship between RBW, VBW and sweep speed. You must have a sufficiently SLOW sweep speed to allow the detectors to property charge up and output the correct amplitude. If you uncouple RBW or go manual, and you select a sweep speed that is too fast, most analyzers will alert you with a "uncal" notification. The same will happen with VBW. The VBW is a low pass filter, if you have a certain sweep speed, the video applied to the screen has certain high frequency components. If you turn down the VBW, you will start to filter out those high frequency components.
The video may be somewhat misleading in stating the VBW will not change noise amplitude. It does not change the noise floor, but it does filter the noise and it will change signal amplitude. Both the RBW and VBW will change signal amplitude if not set properly. If you independantly change, and go too far in turning down (narrowing) the RBW, VBW, or sweep speed, you will start to filter out the sharp peaks. You don't care about the noise, but if there is a very narrow signal peak, whether the signal of interest or another signal off to the side, the VBW will prevent the signal from reaching it's maximum peak. As in the RBW, the analyzer will notify you when your VBW setting is compromising the amplitude accuracy. This applies whether it's an analog or digital analyzer. Leaving the RBW, VBW, and sweep speed in "auto" or "coupled will keep you out of trouble.
Now for averaging. Averaging does not "filter out" the noise, it mathematically adds them together, and as we all know, "true" noise is random, and thus mathematically they eventually disappear after a sufficient number of sweeps. But what does it do to the signal of interest? Nothing. If the signal is stable and there continuously, it will be mathematically reinforced. This includes the most thinnest and sharpest peaks. So averaging does not remove the high frequency components that are really there, only the ones that are random and not there all the time. It's very good at looking at the signal of interest, but it can mask intermittent interfering signals. One note of caution, the analyzer's frequency drift puts a limitation of the amount of averaging that is possible. If the swept bandwidth is moving due to high oscillator drift (as in the older HP8590), the averaging will destroy your signal. This happens by adding sweep copies that are not in the same place; the peak in the current sweep, is moving relative to the location it occupied in the previous sweeps. Note that the analyzer will probably NOT alert you of this condition. Most likely in analyzing a signal, you will be changing all of these parameters at one time or another, this is why you need to know how to operate your instrument, as our video author is trying to convey. Again, well done on the video.
Bob