So here's a huge gaping hole in this so called "theory." According to Ancient Aliens, it is from these mysterious aliens known as "The Nine" that Roddenberry got the ideas for the Federation and the Prime Directive.
Thing is, Roddenberry didn't actually create or develop the Federation. The first time the Federation is mentioned is Arena, with A Taste of Armageddon being the first episode to actually use the full term United Federation of Planets. Gene L Coon wrote the scripts for both episodes. And indeed, a lot of development into what the Federation actually is comes from Journey to Babel (written by DC Fontana) and the movies and 24th century shows, which Roddenberry wasn't involved with. Now you can say that it's Roddenberry's show and the ideas came from him, regardless who wrote the episodes, but it is known fact that a lot of the details of TOS actually did come from people like Gene Coon and DC Fontana.
The Prime Directive is a bit trickier. Wikipedia credits Gene Coon as creating it, noting there's some contention that Theodore Sturgeon was involved as well. However, I am inclined to believe Roddenberry had something to do with its development given the first episode to mention it, Return of the Archons is a Roddenberry-developed story. Also, Roddenberry wrote The Omega Glory, which even though it was filmed and aired in the second season, was actually one of the proposed pilot scripts for TOS.