Seeing and Believing

If they thought he could be Elijah, or John, or one of the prophets, then for them he became those identities.  They saw what they saw and made it so.  Though their understanding may have lacked the accuracy of Peter's, for them it was complete and in accord with what they were ready to believe.  To have seen him instead as Messiah or to have made that their confession would have been lacking in faith.  They saw what they saw and believed in accord with that.