"The best we can do is take Paul at his word - - that Peter was allied with James" (and not the other way around).In the gospel of Matthew, Peter is told by Jesus that he will be given the keys of the kingdom, which Roman Catholics take to indicate that he was put in charge of the Jesus movement. But the transition from Jesus to James to Simon appears to be well documented.
So what were the "keys of the kingdom"? The image is a Biblical one taken from the book of Isaiah. To have the key of David is to be like a chief of staff over a royal household or administration. What Jesus was promising Peter was not succession but that he would occupy the right hand position of responsibility, which he did in service to James who was of the house of David. ~ James Tabor, starting at minute mark 1:11
So who is informing Joseph Smith's understanding? Basically, the Vatican of Rome and its offshoots.
Faith is not built on ignorance.