Someone by the name of Guest posted an "answer" with more details, including key words of "TECT" and "Anaben". A Google Books search for those terms brought up excerpts in James Gunn's The Road to Science Fiction volume 4: From Here to Forever, from which I worked out that it was George Effinger's "The Ghost Writer". Open Library has a copy of Universe 3, which contains that story, and it is a match.
HE WAS performing before several hundred million people, although he himself was the only person in the huge stadium....
Anabben proceeds to indeed perform fragments from ancient works, his consciousness guided by TECT.
It ends as you remember. A young boy tried to access the TECT, but is lost, whereupon Anabben admits he never actually traveled mentally via TECT.
"... I don't merely report, I write. There never was a Sandor Courane. His words are from my mind.".
Then, three "tectman" make him disappear for his sin.