Okay, I've seen these videos a couple of times and I have to say this is pretty risky. I'm a professional area rug cleaner in Tampa FL and I clean hundreds of rugs a year and I can tell you this is not a good way to clean your rug. Even durable synthetic rugs can be damaged by extremely high pH cleaning solutions and high pressure spray, like you find at a do it yourself car wash.
I'm not suggesting that you can't clean your rug yourself, or that get your rug soaking wet while cleaning it. I'm just suggesting that trusting your rug will make it through a cleaning that is designed for an automobile might not be the best idea. I soak rugs all the time to remove unwanted soils and biological contaminants, but I have been trained to do it using solutions that will not harm your rug or put it through unnecessary risk.
Using a high pressure application of soap can damage the color and or texture of a rug. Depending on the rug material it could even tatter the rug, where it falls apart during the drying stage. Now it's completely up to you if you want to take the risk and clean your rug at the DIY car wash, but as a professional area rug cleaner I would not recommend it.