Isn't that a much more general argument? Anytime I do some garden work myself, fix some appliance myself, clean my house, buy groceries, cook my own dinner, do my taxes alone, drive my car myself, etc, I'm not increasing the GDP, but I would be if I paid for the respective service.

Also note how in your first scenario both people earn money, in the second scenario only A does (ending up with more than what B had in scenario 1).