Regardless of the idea that you think it's a waste of money, in heating climates insulation in the basement is often required by code. Normally it's only require 4' in from the rim joist, but some locales require the entire basement ceiling to be insulated.
If you did use a faced insulation, and you're in a heatign climate, you would indeed install it "backwards" with the facing against the underside of the subfloor...towards the conditioned space.
It's easiest to install an unfaced batt. Your inspector likely will not care...but if he wants a vapor barrier, ask him to work up the perm ratings for the platform sandwich (subfloor/underlayment/flooring) that separates the basement from the first floor living space.
If he figures out the answer, there's your vapor barrier.