It is a very common assumption, particularly among educated but stupid people, that formal education is required to make people know things. I agree that in certain specialist areas this may be true(you're unlikely to become a quantum physicist by getting books out of the local libarary), but in most branches of learning a clever person can easily educate themselves. Oxford, Cambridge, and Catholic hotbeds of insurrectionary learning in France, did not have any monopoly of learning.
    McGrath seems totally rigth(as usual), you need to look at the arguments backwards sometimes. It is suggested that no ignorant person could possibly have written those plays, therefore the author must have had a proper rigorous formal classical education. But you can take a different angle on the facts. The author of these plays is obviously an intellectual giant; therefore he didn't need to have had a formal education, he could have learnt it all for himself. Two precisely opposite conclusions from the same piece of data...a rather simple piece of data at that: that there's a lot of clever stuff in the plays of William Shakespeare( or whoever).