I'm not sure that I've ever seen a hole saw with which that would usually be possible, since it's usually the 'centre drill' which connects the cutter to the drill's chuck, isn't it?And it looks like he initially tried to drill it without a centre drill in the arbour (as seems to be evidenced by the excessive scoring).
If the boards are going to be concealed by floor covering, then it doesn't make much difference how one is going to do it - so the easiest/quickest is probably the sensible way to go. However, at least in my experience, if the boards are going to remain at least partially visible, then one can usually end up with an aesthetically better result with such a hole than with cutting across boards (using a saw with a blade of finite width) over joists. Maybe you've never tried but, apart from anything else, it's difficult to chop through the tongues of tightly-butted T+G boards (using any method) without making quite a mess of them.Why on earth didn't he just use an osculating saw to cut the board on the joist.
... and, as aptsys has said, it is quite a common method with chipboard floors.
Kind Regards, John