Unless I recall the wrong source for this, Inside Star Trek has GR and Herb Solow borrowing a print of Forbidden Planet and screening it while they were roughing out the series premise. Supposedly they wanted to ensure they weren't accidentally copying a film that neither man was very familiar with. So they viewed it and were satisfied that it was nothing like their ideas for Star Trek.
There are memos at UCLA that show they not only screened the film, but they sought out its crew and also inquired about frame enlargements from the movie. I can't recall, off the top of my head, what Inside Star Trek has to say about it. What you recall doesn't sound like it, though.
I wrote about this some time ago, actually:
http://startrekfactcheck.blogspot.com/2013/07/gene-roddenberrys-cinematic-influences.html