The qualifications I recommend are your basic racing pit crew safety gear. Helmet, full Nomex suit and a safety man with extinguisher handy. Man, that would be a sight at the local Gas 'n Go!
Seriously, I cannot recommend leaving the engine running. Yes, I've done it too.
First, sparks, spills, etc. could incinerate you, your car, and the station. 6 o'clock news stuff, that!
Second, I heard of cases where someone pulled up, filled up, and left the keys in the ignition. As they went to the window to pay, a low-life slid into the car, now full of fuel, started it and drove off!

With the motor running, it's even easier.
If you have a hard time re-starting it, get it fixed, don't leave it running.
BCingU, Jim
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'96 E300D 60k mi (wife's daily ride)
'95 Audi 90 120k mi
'92 GMC Suburban 139k mi
'85 300SD 234k mi (my daily ride)