I am lucky that my Corgi's fur does not mat, but I have a Border Collie mix with tons of soft long fur who does and we shave her down to 1 inch regularly for the Spring and Summer months since we travel with her to areas where fleas and ticks are potential problems. The fur grows back just fine and fairly quickly. I also have a long haired cat (Maine Coon) whose fur mats in certain areas. I cut the mats out carefully and the fur grows back there easily too. Mats can be very painful as they pull on the skin, which may be why your pup does not want you to touch him. A badly matted dog is a job for a groomer, then you can more easily maintain his coat in proper condition.
Max was a fluffy who had been completely shaved when we got him. His fur grew back just fine from that and also from surgery he had to have. I agree with Anna about letting a groomer handle it. It will be much easier to keep neat and clean after without a lot of hassles.
My son has a dog whose hair mats, even though he brushes and combs regularly. It's difficult and kinda risky to try to cut or shave the mats off yourself. I'm with Anna: take that dog straight to a good professional groomer. Might be a good idea to plan on a grooming job on a regular schedule.
My corgis have never had matting problems.. just occasional shedding in chunks and tufts (as is pretty standard), but my Newfie mix seems to mat up in a matter of minutes. He tolerates brushing, but if the matting gets too bad, I end up just snipping a bit off. He's pretty fluffy so a snip here and there can kind of be covered up and go unnoticed, but there have been a couple times where his butt fluff got so bad that we did indeed have it shaved down. We took him to the groomer for the shaving part because it's a very delicate area and the matting did make some of his skin irritated with how it pulled when he was running/jumping/etc. He went quite a while with not wanting his hindquarters brushed because it had gotten so painful, but the occasional brushing afterwards with treats and lots of petting, he became better at it. It's all about repetition and getting into a routine. Once your pup gets used to the brushings, he'll actually enjoy it! Good luck!!
Yup. It's hair, it will grow back.
By the way, if you go to a groomer be sure to remind them not to pick the dog up in such a way as to injure his back. Corgis, like bassets and Doxies can be injured if picked up wrong. I took my Corgi to a groomer at the VET. They hurt her back and she was on pain pills for two weeks. Her treatments were picked up by the vet but you would think they knew better.
Oh my goodness. That's dreadful! Good reason to learn how to groom the dog oneself. :-(