When I did On Impulse I did it as an entire studio recording from scratch, no original track. I then filmed myself playing along to that and muted the video.
If I was just doing a quick cover, I'd do a live take over the song with my guitar recorded direct (I only use plugins). Webcam audio if I was using an amp.
A layered cover with multiple guitars (splitscreen or not) I'd record in takes over the song, edited if necessary, mixed to an extent. Video overdubbed and muted.
Could say the middle option is the only 'legit' method...but I don't really mind. I guess I'd treat them more like 'music videos' a lot of the time.