Ian,

Your statement is very accurate - Jon Stewart has denied the relationship - multiple times, in fact. However, just denying something doesn't make it true. What actually happened is that there was a rift in the Stewart family several generations ago. While the reasons are lost to the annals of time, the repercussions are still being felt today. According to an article that I read (I can't remember where, now - probably in People or something like that), Jon's branch of the family refuses to have any sort of contact with Martha's branch, and in fact, denies that a relationship exists. Martha's branch of the family will admit to the relationship if pressed, but still refers to them as "those damned carpetbaggers," which may give a clue as to what the nature of the rift actually was.