The Elizabethan times were incredibly well documented. A wealth of records exist in government and the church as well as all manner of public life. There is an incredible lack of evidence in the life of the man from Stratford, given the evidence that is left behind for any of his contemporaries, no matter how poor they were in comparison.
To be able to read the books that are obviously referred to in the Shakespeare canon, you had to have had access to them. Getting access to books was not at all easy. Most were housed in collections of the rich and important and were expensive objects to own. Anyone wishing to read these books would certainly have had to ask permission first, but there is no record of the man from Stratford ever doing so, nor anyone ever granting access.