Looking at this again, I think the video was correct and my understanding of the video was wrong.
I think the white wire is the neutral that is in fact supposed to be connected to the green ground screw (i.e. to the metal frame) as a way of grounding the dryer via the neutral wire. Whereas with a 4-wire connection, this white wire is not actually needed and is therefore screwed to the terminal block’s neutral as a way of safely stowing it neatly somewhere in case it is needed in the future.
Still, this is off topic really.
I think the white wire is the neutral that is in fact supposed to be connected to the green ground screw (i.e. to the metal frame) as a way of grounding the dryer via the neutral wire. Whereas with a 4-wire connection, this white wire is not actually needed and is therefore screwed to the terminal block’s neutral as a way of safely stowing it neatly somewhere in case it is needed in the future.
Still, this is off topic really.