Charlie, I've pulled trailers for years but nothing the size of the 24' I'm pulling now. My wife bought it used, and it came with a weight distributing hitch and sway control. I'm pulling it with a half-ton 2003 Tundra, and the truck's a bit light. The weight distributing hitch is a big help just keeping the truck from sagging so much. But I've pulled it with and without the sway control, and I honestly can't tell that it does anything. The trailer pulls straight, and when I get passed by a semi on the interstate, I can feel it pull the trailer toward it. But as you experienced, I just keep going straight, and the trailer goes where I go.
One thing I've noticed on my Tundra is that the rear sags enough that the steering gets light (I'm taking steps to correct). In the OP, as I remember, the tow vehicle appeared to be severely overloaded. If so and the steering was as light as I suspect, I wondered it the driver may just be constantly over-correcting to keep the tow vehicle in a straight line. As you said, where the tow vehicle goes, so goes the trailer.