Yes, that's right - only paid nights count. If you're on a certificate, using points, or any comp situation - does not count as night's credit. Starwood recently changed their policy (I believe) to include point stays toward their "Elite" status categories, but has not been adopted by Marriott.
Since the gift certificates aren't a comped situation, they could be used towards a counted room. The distinction gets kind of gray there and could be confused, it seems to me. Another thing people will do if they have the Marriott credit card is to buy a gift certificate using the card and getting points for doing so. They are right about free night coupons or point usage towards a room.