I believe--and please correct me if I am wrong, Julia--that the group here is actually talking about 3 different types of certs; 1) gift certs good for a Hyatt stay any night of the week; 2) gift certs for a Hyatt weekend stay, and 3) Hyatt Gift Check certs, which are good for a specific dollar amount.
I believe the difference here is that if you "pay" for your stay with a cert that is good for a complimentary night or a complimentary weekend night (examples #1-#2), then you get no GP points on the "value" of the room, because the room was complimentary based upon the gift check.
However, if you "pay" for part of your charges with a dollar specific gift check cert, then you get GP points on all of the dollars charged to the room act.
I looked into giving these certs as gifts and they are a good deal at some properties--basically if you want to give someone a free week night or a free weekend night, then you'd want to give them a cert that would be good for the cost of the stay. You would not want to intend to give someone cert for a free night, but only have it worth $100, and then find out they booked a room costing $150 and therefore did not get the gift of a free night that you intended.
Of course, if you are buying these certificates for yourself, then you do not have that worry.
But if I am correct in this we can all see how Hyatt can give us points based on a cert that has a specific dollar amount associated with it, but there is no way they could give us points on a cert that was a free, complimentary night--because the computer system at the hotel would show the room revenue for that night as $0.00.