Negative, those VH-60 "White Hawks" belong to and are flown as Marine One as well. HMX -1 is the only Marine unit to have the H-60's to my knowledge.
I believe he means that if the President were riding on an Army UH-60 for whatever reason, then it'd be Army One. Don't know if that'd happen though.
Although, prior to 1976, it was all Army One........no Marine One.