MOST (not all) modern cars use a blend door system for the reasons stated but also because it allows a smaller radiator. The heater core rejects heat just like the radiator and you have to have it anyway so the manufacturers figure you might as well make use of it. The hot air is directed away from the passenger compartment when not needed for heat and thru and into the passenger compartment when you do need it.

Older cars had a water control valve (in American cars called a RANCO valve after the most common manufacturer) that was essentially a cable controlled 1/4 turn ball valve. This was another part that could be eliminated with the blend door system.

So basically, your friend is operating on dated information but he was not completely wrong depending on the vehicle in question. For most current vehicles you are right on the money. I don't know what the bet was but it looks like you're going Dutch!

Dan