The studies that show a poor or zero correlation with MAP may be flawed in that mycobacteria have traditionally been a very difficult bacterial genus with which to work. Koch's postulates have never been fulfilled with leprosy, for example, which is a mycobacterium. They are slow to grow, slow to die, and very tricky to culture; it seems likely that even sensitive PCR tests may not be effective in finding their DNA in many cases; cattle shed much larger quantities of MAP than do humans, and the veterinary tests are substantially more effective than similar tests on human biopsy and fecal samples.
If the correlation between MAP colonization and Crohn's were so poor, then we would not have startling results like those of Warwick Selby, whose anti-mycobacterial protocol put some 95% of patients in remission. Moreover, it would explain why so few of them (perhaps 15%) remained disease-free months or years after the antibiotics were stopped: either they were re-infected with MAP, or the organism was never really gone. Mycobacteria are very slow to grow, and very hard to kill without harming the host. If the gastric environment is not changed (which presumably entails a change in diet to prevent the entire gastric flora from simply combing back, giving an ideal environment for MAP to grow), the disease reoccurs.
Another way of looking at it: take a look at the symptoms of a cow with Johne's disease, which is known to be caused by MAP. Then look at human Crohn's and the symptoms of the disease in us. For those that wish to believe it's a coincidence- more power to you. That's fine by me. But when I lost weight, it was as muscle mass. It wasn't for a couple of years that I finally became overtly sick, and after reading about MAP infection I realized it was more than just similar to the protein-losing enteropathy (PLE) of cattle with Johne's.