I am not aware of any reason why a piston aircraft engine cannot be shut down soon after starting.
This is a really pointless accident, more horrid because the woman passenger probably got her arm chopped off. No pilot should let somebody get out with an engine running, unless the person getting out clearly knows what he or she is doing.
On my first solo, the instructor did a few circuits with me, and then got out with the engine still running, but obviously got off to the rear and not towards the prop. In fact I did my "first solo" twice (because I changed schools c. the 20hr point) and the 2nd instructor also got out with the engine running.