Well, Stan Lee's own account from ORIGINS OF MARVEL COMICS backs that assertion. Lee describes in the post-EC comics code slump period from 1960-1961 that he was golfing with Martin Goodman, and he told Lee that JUSTICE LEAGUE was outselling everything for DC, and to come up with a similar superhero group for Marvel.
By Lee's account, he came up with everything, and assigned Kirby to draw it.
By Kirby's account, he came up with everything and had Stan Lee script it.
Either way FF number 1 came out in Nov 1961.
I understand Goodman had a much wider line of magazines, including porn, beyond Marvel/Atlas. There was an article on Goodman in one of the COMIC BOOK ARTIST issues, pretty long, about 8 or 10 pages.