Why would it be unsanitary? You aren't using the paper cup yourself, by lifting it to your mouth or touching it at all.

I think a quick rinse at most would suffice between uses of this paper cup, which I'm sure was used to measure portion sizes. I guarantee you plenty of people showed up with their Bubba Kegs trying to make the most of a discount on a travel mug, and were disappointed it wasn't filled to the brim.