When I read "The Arena" short story by Brown in a science fiction collection I immediately thought it was the basis for the episode. I had no doubt. It was virtually the same story as the second half of Arena. I'm very surprised when its denied. I must have read the story 10 years after seeing the episode but still made the connection.
Since when did they deny it? It is pretty much established that Coon was reminded of the connection after he wrote it - and put it in the production pipeline. They went to Brown, gave him some cash, and gave him story credit.
And apparently, Kellam de Forrest had very little problems with Tribbles, otherwise they would have said something.