Veltz and Kanoi,
There is no such thing as perfect knowledge and almost nothing can be proven as fact with 100% certitude.
Accordingly it would be absurd to require a shliach tzibbur (or anyone for that matter) to believe anything without doubts. That is why in American Law there is a concept of beyond a reasonable doubt for criminal convictions. However, in civil cases the standard is more probable than not (aka preponderance of the evidence) which means 50+ epsilon.
I think that there can be little argument that someone who believes that it is more probable than not that the Torah is true and lives his life accordingly, is eligible to be the shliach tzibbur.
The question is someone who is basing his/her Torah true lifestyle on something like Pascal’s Wager or to remain within the community he/she loves.