I've heard it mention before, and this answer by pfw did me think about it again. What is the klebsiella bacteria and what is its importance (and for whom)?
Here's a blog post I wrote explaining why it matters for Crohn's sufferers. It's a bit much to reproduce here. Also, I should add a disclaimer that I'm pretty sure I'm not precisely/accurately describing the auto-immune triggering mechanism. The basic gist is that the bacteria produces proteins which mimic proteins in your body, so when your body mounts an immune response to them, the immune response ends up attacking some of your tissue as well.
There are a whole host of auto-immune disorders for which the diet->bacteria->mimetic->disorder hypothesis has very intriguing implications. Any auto-immune disorder could be explained via this mechanism (substituting in different bacteria and different proteins being mimicked), and while that certainly doesn't mean that all auto-immune disorders are the result of this sort of thing, it does provide an interesting avenue of study for many of them. Especially because you can potentially provide relief through diet, which is a far superior solution, in my opinion at least, than lifetime application of drugs.
There's a ton of papers out there by Ebringer and his team devoted to explaining and testing different aspects of the connection between KP and AS/Crohn's.
1) HLA-B27 Positive/Negative: I believe that this just means you produce the HLA-B27 antigen or not. If you do, that marks you as someone who is likely to get AS. If you don't, that marks you as someone likely to get Crohn's. Could be wrong on this point. Basically, the point is that the particular part of your body affected has to do with the way your body tissue "looks" to the immune system, which is all about protein sequences/genetics.
2) Leaky Gut: This means that the boundary between the "outside" of your bowels (the part with all the digesting material) and the "inside" (you, basically) is not completely blocking the entry of foreign proteins. I suspect that everyone has a leaky gut to some degree. This can be made worse by sensitivity to grains and dairy - probably any allergy, really - and it can also be induced through direct injury. I recall reading somewhere that people who have been in car accidents are much more likely to get Crohn's. One might explain that fact by observing that the sudden acceleration in a car accident could cause micro-trauma to the gut lining, allowing foreign proteins in and initiating an immune response.
3) Fiber versus starch: I don't know! Starch is clearly capable of causing problems, and it's the target of the diet. Fiber is a different beast. I avoid it mostly because I'm not sure how it is broken down. If fiber is fermented, and starch freed up or produced because of that fermentation, you get undigested starch in the colon, which is what you're trying to avoid. Maybe avoiding fiber isn't necessary at all. Thankfully, fiber itself doesn't appear necessary, so I don't worry about this by not eating it ;)
4) Psoriasis: My father actually has psoriasis. He had a really bad flare up a few years ago and jumped on any treatment he could to get off of it. He tried a gluten free diet for a while, sun treatments, medications, you name it. Eventually, the flare up died down and he's back to sort of normal. He's eating gluten again and ascribes his getting better to the light treatments. IF you get a lot of sun exposure, maybe you're helping yourself out already.
I did read in one paper that AS and psoriasis were present in people with KP overgrowth, and generally I see arthritis and psoriasis linked. This might suggest a link with KP along the same lines as in AS and Crohn's. You could try a no-starch diet for a while and see how it works for you - nothing to lose really - but I would caution against drawing too strong a conclusion from this stuff. What I've read focuses on Crohn's and the specific mechanism by which intestinal collagen is targeted. I don't know any mechanism by which your skin might become the target of an immune response. As I said above, it's plausible that any auto-immune response could be caused by something similar, but I just don't know of any research showing it with psoriasis.