He's just talking bullshit then?
Yes and no. The 750-1200 W power supplies will fit like he states. If you take a look at the bottom of the case you will see that it is completely open all the way to the hard drive bays. The only limiting factor for a power supply you will find in a case is the available room for the power supply. As long as there is room anything will work.
A MB is 9.6 inches wide. There is a point in that video where you see him put his fingers behind the MB tray. If you look at that point you will see that the MB tray extends past the MB by about an inch. There is also an inch or two past that where he fits his hand in. That is where the drive bays start, which leave around 11 - 12 inches of room for the power supply. Of course you lose a couple of inches to place the power cables themselves but that is more than enough room for any ATX power supply I have seen.