Not a Raptor specifically, but a buddy of mine has a F-150 SCREW that had a similar wet carpet issue. Turned out that behind the rear seat, on the back wall of the cab, there are two vents to the outside, these relieve air pressure when you close the doors. These vents are really just slatted openings with light pieces of rubber (flaps) laying over them. When you close the door internal pressure blows the rubber flap open and vents the air.
In his case one of the light rubber flaps had curled up, and was open all the time. When it rained (not common in the desert, so it took a while for him to figure out what was happening) the rain dripped / flowed down the back of the cab and in via the curled up flap. Flowed down the inside back wall, and down behind / under the carpet.
T!