And the historical, literary and Biblical references in Shakespeare are of heroic scope. It would be inaccurate to describe the author(s) of those plays as un-schooled, it seems to me.
Churchill was not un-schooled, nor is Gates (even though he dropped out). And neither Gates nor Ford nor Branson are known for their knowledge of history or literature or the Bible or such stuff, knowledge which comes from prolonged study and meditation on the material.
Still, I take your point...
Check out the following link. Good food for thought...
http://home.att.net/~tleary/twain2.htm
I seem to remember having read somewhere that Shakespeare's family was Catholic, though not publicly. It is possible that he was educated, privately, by a priest, as many young Catholic men were in that time. If he had been taught to read, and took to it with relish, that could account for his not having attended school as his Protestant peers had done, but having had the knowledge of the Classics that they had.
I believe Shakesperare was Francis Bacon, who was an embodiment of the Counte de St. Germain, Wonderman of Europe, and that Bacon received his divine inspiration from (Saint) Pallas Athena, known as the Goddess of Truth, often portrayed holding a spear. Thus Bacon used the name, "Will (of God) I Am, Shaking the Spear (of Truth).