Well, that Inside Star Trek
account doesn't address the question of whether Coon might have read or heard about Brown's story years before, which is the sort of thing that would have happened if "Gene Coon was concerned he may have been influenced
by Brown's story" as Christopher
first put it (emphasis mine). All we can glean from that account is that, if he had, he had honestly forgotten about it. Which is fine; it makes no difference, since he and the producers did the right thing.
I've also noticed "story by" credits, such as for TNG: Sarek
where it says story by Peter S. Beagle (from an unpublished story by Marc Cushman & Jake Jacobs). So, I guess the case there is that material originally conceived in some for or another for Star Trek