Whether you go to the front desk or not, I assume you received a folio under the door. And if you had a paid night followed by a free night, you would have received two distinct folios. In many instances of a free stay after a paid stay (or vice versa), things get screwed up. Did you bother to review the folios? I don't mean to be harsh but it was your responsibility to review the folio before leaving the property.
Look at the bright side, after you get the money part straightened out (which should be easy as the points were taken out of your account and your email copy of your reservation should have said SPG Award), you will have 2 nights not just 1. SPG probably won't go back and take away your night.
Ah, that's the rub. There was no folio slipped under the door either night. And a copy of the folio that was faxed to me this morning shows one folio with one total. Weird I agree, but the billing error is clearly their issue not mine.