Laying on someone is fighting is it? No
Is striking fighting? Yes
Is BJJ fighting? Yes
Laying on someone will never ever result in a finish without striking or submissions, so don't lay there not doing anything, that's not a fight that's a game of control.
His argument is utter bullshit.
controlling someone for 15 mins is more convincing than getting a guillotine or flash KO.
Finishing fights has nothing to do with it you dont finish fights with rubber guard you use it to gain control for other things to finish the fight like wrestling.