I've never before seen 10-20 weight oil. Regardless of that, I would INSIST that they put in what you specified, or don't pay them.
This is an ABSOLUTE PREMIUM PRICE for an oil change, I don't care what oil you're putting in. Two gallons of Mobil One is only about $40 worth.
I would never use oil that light in any engine if you are South of the Arctic Circle.
Best of luck,