The JSP is the Bible and cannot be challenged. All you can challenge is that you do not have the diagnosis present in your medical notes. Appeals are reviewed by a Service MO but it is a paper process. Hard to give you exact figures regarding success as it depends on what your issue is, but bear in mind that we have loads of applicants at present and the onus is on the individual to prove they are the same standard as someone with a clean bill of health.
Whilst not qualified to offer medical advice, it's worth bearing in mind the JSP, as the name implies, is Joint Service - the Naval Service also operates a single service policy in some areas and they maybe more stringent. In short, that means a person cannot appeal against a single service standard that doesn't apply to other services in the JSP.