Secretariat's nickname was not only because of his color, but in tribute to his ancestor, Man O' War.
Man O' War, from all accounts, was a nasty sumbitch. He passed that temperament, as well as his blazing speed, onto his progeny.
War Admiral and Hard Tack were sons of his, and Seabiscuit was Hard Tack's son, so Man O' War was his grandsire.
It's difficult to find any horse with TB in its pedigree that doesn't have a line back to Man O' War.
It's like the Arabian breed today; it's a surprise if you don't find a horse who is related to Bask, Khemosabi, or both.