It varies from band to band, although it is indeed most common by far to follow the drummer's tempo and rhythm.
One exception I know of is Black Sabbath (original lineup), in which everyone followed Tony Iommi.
These youngsters simply need to decide who gets to drive the bus. Based on their videos, it is clear that the guitarist is the best musician and has the most precise rhythm. If the others learn to follow him, they'll sound better. (It looks like they're trying to do that, but haven't got it down yet.)
However, this does not mean the guitarist can do whatever he wants. Until the other guys in the band can keep up with him, he must learn to watch them and see when the band has gone out of sync. When that happens, the best idea is for everyone to sync themselves up with the drummer, even if the drummer is wrong. A listener tends to perceive the drums as defining the rhythm, so the other musicians have to let the drummer take that role sometimes.
As an example from my own band's experiences: our drummer has a tendency to speed up slowly over the course of a song. Rather than try and get him to slow back down, it's much easier - and sounds better - when the rest of us speed up to match him.
