The second pilot is more focused on action, features no self-doubting protagonist and fewer women. So Roddenberry's claims seem fairly consistent whereas you story about the studio wanting proof that the show could be done with a smaller budget seems fishy. Why not simply cut the budget, air the pilot and shoot the series instead of wasting an entire pilot? No, they obviously wanted an admittedly only slightly different product.
Why doubt what's been reported by multiple sources over the years?
And why do people care about Roddenberry's sex life?
Not so much about his sex life but how he treated women while preaching about a better future. Sort of like a religious figure preaching against homosexuality then being found gobbling a snake on the Men's Room floor.
Roddenberry had a great vision, but the guy was a creep. A proven liar, thief and adulterer.