The driver doesn't get paid less than minimum wage, or at least at Papa John's they don't. Well, while they are "on the road" they do, but while they are standing in the store they don't.
It is true that it might not have been the driver's fault. It was more than likely the stores fault, and what ever idiot you talked to tried to cover and throw the driver under the bus. The most suspicious part of the story is that the driver only had $5. Generally each driver gets a "bank," of 2 $5 bills and 10 $1 bills. As they go on through the night, they have more and less change, but I usually tried to keep at least $20 in change all night. Delivery drivers get a lot of shit from stuff that isn't their fault. If he really only had $5, then tough cookies for him. Even though I spent years delivering pizza on and off, and liked getting tipped as much as the next guy, I wouldn't have expected a tip for screwed up order.

Conclusion: If you are upset at the store, punishing the driver is the wrong way to go. Just stop giving that store your money. Personally, I don't order pizza at all any more because EVERYONE has bullshit "delivery fees" that DO NOT go to the driver. People think they do, then stiff the driver, or yell at them over the fees. Also, 3 miles away is REALLY far for a delivery. Actually it is stupid far. You are probably on the very edge of their delivery range and the drivers likely hate going on singles that far from the store.