A while back my friend said that moving with the analog stick and looking with a mouse can provide a serious advantage for movement. Is this allowed for running?

If you look both M+KvsController in some records, you will notice that m+K is far superior than a controller. That's why the leaderboards are separated.

He means using the controller with your left hand for movement and the mouse with your right for aiming. Not unheard of in other console fps games but is it fair for speedrunning? I dunno.