People must remember that the reason why the sports world was cheated out of Secretariat running as a 4 year old was because federal inheritance laws required the Chenery heirs to raise money quickly. Ravenous government sent him to the sidelines. Up to then, the Chenerys had raced their prospective studs (including Riva Ridge, the previous year’s Kentucky Derby winner).
So the movie is truthful in that respect.
PS. Still, Citation was the best horse of the 20th Century, followed by Man o’ War.