That's one big girl! She definitely looks like she doesn't have anything but draft in her. The interesting part is she still has her tail. If she were PB percheron, she most likely would of had it docked. One senario could be that she's a solid spotted draft (more commonly not docked). Another would be that she is full percheron but a QH cleanup stallion as put in with the mares and based on her foaling date, they concluded that the QH was her sire. (If something happens to the stallion running with a band of mares, he is removed and another stallion is added to the group)
How old is she? The one farm in ND that I've visited, Bryant's, was raising B/W spotted drafts out of registered percheron mares. They were the largest PMU ranch around but they've been out of business for about 5 years. If she's 10ish, she could of come from a Natural Biological farm and they were all shut down 8-10 years ago. Those breeding programs were all over the place. If she came off a NAERIC farm, she could be microchipped. The brand didn't come from the outfitters? PMU farms would of only branded her (and it would of been a # to help identify her) if she was on the line, CA doesn't typically brand, and the rescues definitely wouldn't.