For a while now I've been fond of the notion that the Jedi had much humbler beginnings than the contrived nonsense from the EU.
What are their origins in the EU. As far as I know, there are only a few books about the subject that came out around 2011-12. They take place 25,000 BBY and feature the Jedaii, and describe some pretty humble origins.
Edit: Really, anything that happened 25,000 would be steeped in mythology. Thinking about our own history, we only have records going back 3 or 4000 years, and even those are steeped in mythology. In the above mentioned books(it may just be one book-the start of a series that was discontinued), I don't think they yet have space travel.
A reason I don't particularly care for the whole Coruscant "Sith shrine that predates the Jedi" is because of the Idea that when the Jedi "schism" happened, what would become the Sith fled to Korriban/Moraband, and established themselves there. The Jedi went on to establish themselves on Coruscant after having to abandon Tython. The Sith went on to create an empire, and the Jedi helped create a republic, and the two groups grew up separately. They don't know of each others existence for a long time, but eventually they make contact with each other and a series of wars happen over a few thousand years, until finally the Jedi defeat them once and for all 1000 years before the main story begins.
And in the main story of course, the Sith are trying a new strategy; to take over the Republic from within. To make the Jedi capital their capital. The Jedi can't conceive this because they are still trying to fight the Sith of old. They only know how to prepare for the last war.
Also, the Jedi were supposedly unaware that their temple was even on a Sith shrine. There's already Yavin 4, where a Jedi temple was built on a Sith shrine, and Dagobah, where Yoda went to a formerly Sithy place to hide his presence. It's just another thing that kind the sullies the Jedi's good name, and makes them look like idiots. Sure, a big theme of the Prequels is that the Jedi have become complacent, but they weren't always that way.