The video is very misleading but also quite typical of the misinformation on optics among photographers.
From the presenter's example at 3:11,
subject size, subject distance, fstop, shutter, ISO are the same but the background is blurrer for FF compared to MFT.
So he concluded that same f-stop produce different DOF for different sensor size?
But what about the effect of focal length on DOF?
He forgot he had doubled his focal length on the FF to get the same framing as the MFT.
Multiplying the aperture by the crop factor is downright crazy considering the implications:
M43 shooters must use a slower shutter speed for their f2.8 MFT lenses vs their f2.8 FF lenses?
A 50mm f1.4 full frame lens will give M43 shooter shallower DOF than a 50mm f1.4 M43 lens?
Clearly, it is illogical.
I think, his message is: don't expect to use the same lens to get the same results with cropped sensors.
But his suggestion to label APS-C /MFT lenses against mathematical convention is seriously flawed.
Just imagine what the aperture rating for compact cameras will be using his math. 2mm /f128 anyone?
For the real formula:
http://en.wikipedia.org/wiki/F-number