The cotton foundation could potentially cause browning.
Stanley may have sown the seeds of you owning the problem. But then again you may get away with it if using very low moisture and cleaning on the acid side. One way to do it is letting it dry upside down so browning if happens goes to foundation.
Do a burn test on all the fibers. I realize that the brown fiber might look like jute, but seen similar rugs that were all poly, even the jute looking fiber.
I'm getting better at cleaning problem rugs that I use to run away from. Wet cleaned a sisal rug that had diarrhea on it. It cleaned up fine. Even have good luck with rayon rugs. Seems Hot water is our enemy on some rugs.