Why a Jeep Owner Is Being Sued for a Mechanic's Death During a Dealership Oil Change

Jeep owner had nothing to do with this OTHER than making the mistake of trusting a poorly run dealership to repair/maintain vehicle. A dealership OWNER....SHOULD be responsible for all employees actions while on the clock, or is my thinking too logical?
You are correct

I think the owner of the jeep could then turn around and sue the dealership

It is backwards, but thats what the excess of lawyers and litigation has turned things into