Of course GM's are responsible for players behavior. They inspire them, engage them, thrill them. OR not. Or they don't and then players fiddle with their phones. I've been a player like that - some sessions were so boring I was seriously considering going home. Why sugar coat it?
that's not what he means.
of course sometimes gms don't do a good job. this happens a lot. being a good gm is hard.
gms can bore players. this boredom can lead to players doing stuff while at the table.
but it doesn't have to. they could also speak up. they could say what is bothering them, so the game can improve. they could try to act in a way to improve the game by themselves (sometimes players are too passive and that leads to boredom).
the gm might be responsible for a bad game, but isn't responsible for how the players react to that game. they are.
Fair point Shlominus. However OP is a the GM here looking for advice not his players.