Yes, sometimes healing takes place... but I can't tell you why, or how, or who it is likely to work in and who it's not. So for now, it's not medicine. It's barely a folk remedy. It could be just luck, and I've not seen anything to elevate the "effects" of magnetic therapy above the level of luck.
My experience transcribing clinic notes in an Ortho Surg department (for about a year) involved one really fun note dictated by a surgeon who was happy to see the patient's shoulder ROM had increased significantly, and pain had decreased significantly. He couldn't explain it, but hey, what the heck. Patient feels better, we consider this to be a good thing. Obviously, if there were dozens of others who tried magnets and didn't get relief, we may or may not have made a comment about them.
I also have arthritis in the tarsal and metatarsal joints of my right foot, greater than left. It's well-controlled now (thanks, Enbrel!), but for a while I tried everything, which is of course what patients do. Magnetic insoles, worn for 2 weeks, did bupkus for me.