Right on both counts: he's an ignorant troll.
I'm not even sure Greater Manchester even exists as an administrative area these days.
Salford is not in the City of Manchester. Period.
It is in the metropolitan county of Greater Manchester, which causes the confusion. If the whole of the conurbation that is centred on Manchester had been completely in Lancashire then the new county would have been called South Lancashire, along similar lines as West and South Yorkshire. If West Yorkshire had been called Greater Leeds then you would probably now have threads saying that Bradford was in Leeds.
Greater Manchester still exists as a county, and as a basis for administering the police and fire services.