I have actually gotten some great deals from 3rd party sites from NYC to Negril. The airline costs are about the same but the bigger reduction comes when you book room and air-- usually room costs are significantly less than what the resorts show on their websites. And then I often use a promo code which will take another 50 to 100$ off the package price. I have done this staying at Bar B Barn, NBCC (back when they did online bookings)Mariners and Samsara and got a much better deal than I could have booking myself. But I have also gotten below published rates for Bar B Barn, Whitesands, and NBCC booking myself. I stayed at Country Country and Seastar for their web rate and dealt with them no problem, and got the best rooms.

So I have had success both ways. I have never been bumped before-- but I usually travel off-peak season which helps with good rates and no one full enough to bump.