The debate went on long before there were talk shows--in 1592, a dramatist named Robert Greene published a story, Greene's Groatsworth of Wit, in pamphlet form, about a thinly disguised, disgraced young dramatist who is asked by a wealthy actor to write plays, which the actor takes credit for--the actor was an even more thinly disguised Shakespeare-Greene and George Peale seem to have written the original versions of all three parts of "Henry VI"--Even Ben Jonson, in an epigram called "On Poet-Ape", says "To a little wealth and credit on the scene, He takes up all, and makes each man's wit his own"--
The questions about the authorship of Shakespeare seem to be about as old as the works themselves--