Turbo

I'd want to hear the explanation of how the fuel pump is related to the turbocharger. The fuel pump is inside the gas tank, so if anything in the assembly was leaking, the gas would spill right back into the tank. If there was a leak in a line outside the tank, you would have smelled gas, and there would have been wet spots on the ground. A major gas leak, such as from a ruptured rubber hose, would cause the engine to stall. It can't run without fuel pressure. That would have caused the turbo to stop too, and nothing else would have been damaged.

If you aren't provided a suitable explanation, I would get a second opinion from a different shop.

The fuel pump is in the gas tank. I suspect the mechanic is referring to the oil pump, which IS inside the engine. If there was a service writer at the shop, they are "go-betweens" that take what they think they heard from the mechanic, and interpret it into something they think customers will understand. Often those service writers are not car experts, and things get lost in translation. They are not trying to defraud or deceive, but they are responsible for a lot of miscommunication, and therefore, mistrust of the entire industry.