I in no way will claim to be an expert on this, but I can point out obvious problems with that website you posted, tlong.
First, dmso.org is obviously an advocacy site. Not that they're necessarily wrong, but you have to start with the presumption that they work with a bias. The fact that they go way overboard in claiming that DMSO works for just about everything makes it hard for me to believe them as a reference source. There are lots of well-done studies out there that were unable to show it doesn't have an effect, which conveniently they ignore. Believe me, if there was really that much overwhelming hard evidence, physicians would use it.
Second, the author of that information is a guy who, in the very first sentence, is tooting his own horn about how he was the father of DMSO 40 years ago. So clearly he has a vested interest (professional and perhaps financially) in making it sound like it's a wonder drug. He apparently has a good deal of stature at a very well respected medical facility, so he's not a quack, but that doens't mean he's right. Most importantly, he's a surgeon, and I'd be surprised if he had much experience with all of the non-surgical illnesses he claims DMSO works with.
That list of diseases he gives at the end is laughable. Some of those are some of the most complex and difficult autoimmune diseases to treat and people have tried tons of things looking for answers. If DMSO clearly worked, it would be used.