Like the bringing Lazarus back from the dead, or turning water into wine, or perhaps the Resurrection?
The events you listed were used to establish the whole God / Son of God premise. Most people with a literal belief in the Bible believe that these events happened exactly as written. My opinion is that if you really believe the big events like these then you don't need a bleeding statue for it all to make sense.
Compare:
You accept the idea of Lazarus rising from the dead at the hand of Jesus - you become a believer.
You witness the statue of St. Lenny the Flatulent sweating profusely - you adjust the air conditioner.