Sure. They do it every day. It’s not good for the rug to blast hot water under very high pressure into it, but lots of people; including the carpet cleaners themselves, don’t understand the process of properly removing the dry soil from your rug first. So, they are driving that dry soil deeper into the foundation fibers of your rug. As you already know, dry soil mixed with water makes mud. The surface will look clean for a short while until this mud works its way back up to the face yarns where you will see “returning spots”. This is the dirt that never left your rug in the first place.
Your rug will feel stiff now partly because of the “new” dirt and partly because of the high pH carpet cleaning chemicals that were used on your rug. There IS a difference. It takes about 8 hours to dry a wool rug in the best of circumstances which would be a rug drying room with ultra low humidity and a controlled temperature with lots of air movement. In your home, or outside it can take days for a rug to dry completely. Remember that wool can feel dry and still be damp enough to foster the growth of mold and mildew.
Lots of carpet cleaning companies will pick up your rug and take it to their shop for cleaning. The problem with this is the rug will be cleaned just like carpet, just in a different location. If the carpet cleaning company has the word “steam” in their name, or they will “steam clean” your carpets, they are very likely to use the same equipment to clean your rug.
Often, the carpet cleaner that finished his or her schedule early and gets back to the shop first is the person that will be cleaning the rugs… that day. It just makes sense to hire a company whose sole focus is rug cleaning and nothing else to distract them from that. You can tell the difference and so can your rug.