Okay, sorry I forgot to check back on this thread.
Yes, the pic of that plastic piece is the part I was referring to. All you need do is remove the screws and seal them. Silicone will do fine.
The weatherstrip that had the rusty end on it.....that may well be your problem. Esp. since the plastic clips are wet.
To prove it, you'll need to have a hose running over that door....I usually run the hose over the hood and under one of the wiper arms, and lay it on the windshield or the roof....depending on how much water pressure that particular dealership has. That way you don't need someone to hold it for you.
So have the water cascading all over the door...it'll follow the outline of the door, and also will do down the window and prove out the door drain theory, too.
Get in from the other side of the truck with a flashlight....you might need the kick panel/rocker panel (aren't they one-piece on that truck?) removed....in fact, you DO need it off. And watch the bottom of that door, and the curved part of the door opening just under the weatherstrip. Give it a good little while...not just a few minutes, to start. If that's your problem, you'll see the water coming from under the weatherstrip.
Would also help to have the carpet pulled back so you can see if a puddle is forming from elsewhere.
By having the water cascading over the door and back down the windshield, you'll also be testing that plastic weatherstrip mount.
Let me know how it goes.