and it provides no clear method for correcting what it gets wrong.
Sure it does... kind of: personal experience.
The Buddha told his disciples to examine his teachings, and if something he taught turned out to be wrong, to discard it.
Plenty of Hindu teachers encourage not accepting anything blindly. "Don't believe in God until you meet him," they say. ^_^
The thing is, this is only good for individuals; it's not effective for humanity's collective knowledge.