I suspect that I'm not seeing what I'm meant to be seeing

The door strip is wet and it looks like the water is getting past it into the car. I'd suspect it isn't pressing against the door snugly enough to stop the water somewhere. It might help if you clean all the door shuts, mud doesn't make such a good seal

Is that mud or something nastier? I think all that seal does is stop the water going under the door and leaving the "tread" covered in mud. It's biggest issue is when the clips are missing and the water pours into the sill but it doesn't actually have anything to do with keeping water out of the car.

That door check looks rather wet, I can see the drain looks clear but is the door filling up with water? Is the seal against the glass really loose? so that water is gushing past it into the door?

Plant potatoes here

It looks like the weather seal is pressing quite nicely against the door anyway.