They don't need confidence when they have faith, faith can move mountains and allow them to believe anything.The "written record" as you call it are the words written by man. As you state, no one knows for sure what their motivations were for sure in what they wrote etc.. We do know, the NT specifically (the gospels) were not penned until 40+ years after Jesus died and by UNKNOWN authors. We also know the originals do not exist and only copies of copies of copies starting about the 2nd century. Scholars have also shown, some stories in the gospels did not exist in the oldest copies available and some were added centuries later.
All in all, the "written record" you speak of, does not promote a high degree of confidence in scholars and historians as to it's historical reliability.
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