Conspiracy theories in general, and the "n% of people doubt the story" claims in particular, also appeal to a sense of rebellion in people.
As Wikipedia puts it, "a rebellion is, in the most general sense, a refusal to accept authority."
People don't want to be sheep who are patronized by authority and told what they have to do and how they have to think. People usually distrust authorities and many believe that authorities are selfish and abuse people for their own benefit. This is an extremely fertile ground for conspiracy theories.
This is so ingrained in people that a sentence like "the official story" has basically become a synonym for "a coverup/lie". Whenever "the official story" is mentioned, it immediately makes people think that it's some kind of coverup, something not true.
Conspiracy theorists are masters at abusing this psyhcological phenomenon for their advantage. They basically insinuate that "if you believe the official story then you are gullible because you are being lied to". They want to make it feel that doubting the original story is a sign of intelligence and logical thinking. However, believing a conspiracy theory usually shows, quite ironically, a great lack of logical thinking.
