Basically Dave ask the guy would you take out a mortgage on a paid off home to invest the borrowed money. He easily says no but would consider taking the money he currently has that could pay off his mortgage to invest it while keeping the mortgage.
I see people all the time talk about taking out car loans and investing the money they would have bought the car with. Aren't investments supposed to be from disposable income? That's how I always saw it. You take money you can afford to lose and invest it rather than using loans to live outside your means and enable you to invest money that really would have been spend elsewhere.