Pinching the line will not hurt a darn thing. There is no stress on the engine at idle and simply eliminating the fuel supply does a couple things: it empties the crankcase and carb of unburnt fuel so you will not get any dried up oil buggers in the mixture passages in the carb and no puddles of methanol based fuel in the case which will absorb moisture and contribute to corrosion.
If you pinch off the line, you will not starve the engine of lubricant since there will always be a slick film of lube on all the internals.
Do this: Pinch the line to shut it down and then take the engine apart or at least the backplate off, you will see that the pinch thing is nothing to worry about.