Yeah it would be crossing a line and make him look really stupid, and destroy his whole character arc in Raiders.
It would make him seem like those people in the X-Files or Doctor Who who no mater how much really weird stuff they see they still don't believe Mulder or The Doctor when they try to warn them that something strange is going on. How much weird crap do you have to see before you figure out that you exist in a universe where weird crap happens every day?