The Difference Between Knowing and Believing
When Joseph and Oliver commissioned the twelve, they said they were indebted to others for the evidence on which they acted, and they would be until they spoke with God face-to-face.
These twelve, until they obtained this knowledge, only had the Gift of the Spirit to believe on the words of those who knew. We would also have eternal life if we knew Jesus Christ is the Son of God.
"To some it is given by the Holy Ghost to know that Jesus Christ is the Son of God, and that he was crucified for the sins of the world. To others it is given to believe on their words, that they also might have eternal life if they continue faithful." (D&C 46:13-14)
"And this is life eternal, that they might know thee the only true God, and Jesus Christ, whom thou hast sent." (John 17:3)