Fascinating. I had always assumed that "Arena" was indeed based on the Brown story, probably because the 1973 David Gerrold book stated it as a fact: "And one of the scripts was based on a short story by Fredric Brown."
Ah, interesting. Which book, by the way? There are two Gerrold Star Trek
books from 1973: The World of Star Trek
and The Trouble with Tribbles.
And, do you have a page number?