For one thing people back then didn't write very much because of their education level. They passed on information by word of mouth. They also had greater memories for this type of stuff. Look at the 3 music masters. Bach, Beethoven, and Brahms. They could go to a symphony, listen to it once and go home and play it. People could remember information just about word for word back then.
Also just because something wasn't written down, and proven by science, doesn't mean it's not true. Look at all the natural remedies promoted at curezone. And in the case with natural cures, Science doesn't even want to look at it. Like I've always said, it's Science that's flawed. So you can use Science to prove or disprove God, or prove or disprove alternative methods. I will rely on personal experience over science any day.
To quote one of the greatest scientific minds, Einstein.
"The only source of knowledge is experience"
"Education is what remains after one has forgotten everything he learned in school."
"As far as the laws of mathematics refer to reality, they are not certain, as far as they are certain, they do not refer to reality."
"Not everything that counts can be counted, and not everything that can be counted counts."
"When the solution is simple, God is answering."