Running out of gas should not damage the engine, however, if one were to keep trying to start the engine with no gas, the fuel pump may be damaged. I agree though, you're probably fine. BTW, ever tried to turn the steering wheel on this car without the engine running? Holy cow is it hard. I hope I never loose power on a tight turn.
I had engine stopped "couple" times on very busy I-95, close to Miami, Camsensor bad=Phase, did change "wrong" sensors before, on a top, valve timing sensors, had a really hard time in that traffic....with engine stopped...., but....I am still here ;o)