Can a new radiator cap cause a vehicle not to start?

Okay, I know I'm going to ge laughed at here, but a friend told me that they went to a repair place cuz their car wouldn't start and the tech asked him if he'd just installed a new radiator cap and he had. The tech put a different cap on the vehicle and it started fine, he said that if the cap isn't rated at the correct pressure for the vehicle it would cause starting problems! Me myself I don't see how the radiator would have anything to do with the starting system, but I'm no expert. Anybody ever heard of this before?

If that beast really exist I want to meet it. Just kidding

I know that some vehicles are equipped with a coolant level indicator and if coolant is low it wont allow the engine to start in fear of overheating, so maybe if your friends car is equipped with this type of set up and the wrong cap was installed not allowing to hold sufficient pressure and causing coolant to overflow into the overflow resivoir then maybe this theory is not so silly because if coolant is dumping out of the radiator into the overflow bottle = low colant level = no start.