I didn't see him try it, so....
It must be possible to put it in DFU mode. Just turn it off first and hold the buttons.
A DFU won't fix the Jan 1 1970 bug. The only way to get your phone back is to physically open up the phone and unplug the battery to reset the PRAM. Or you can let the battery fully drain and let it sit for a bit which should also reset the PRAM.