Christianity is about trusting in Christ for salvation. You cannot trust that Christ's saving work on your behalf actually happened or is good enough to do the job if you cannot trust the author of statements to that effect. Why should anyone believe that Christ's atonement is actually able to save anyone if in the same book that is written in, there are stories that are verifiably false?
Well, if you're just talking about born again saved by faith in christ christians, then I think you're right. They've built a house of cards faith that rests on the Bible contianing no errors at all and if errors are found then that whole thing comes tumbling down.
But there are other types of christians than that too.