Pfft.
On the track with no rabbit and with somewhat equal carrying weights, the Good Doctor would set a pace that Big Red would just not be able to overcome, my friend (Secretariat lost his races to horses that set a fast pace at the beginning and led wire to wire..e.g. Onion, Angle Light, who aren't exactly elite quality horses like Damascus or Buckpasser), unless it's a distance race like Belmont, then maybe...But hey, if the two did run together at Belmont and Big Red overtook the Good Doctor on the last turn, well shoot, Big Red is liable to have a huge chunk taken out of his ass when their coming down the stretch.
I'll give you the Belmont run, though, because that was something exceptional, but Secretariat's running times at Churchill Downs and Pimlico that year may be a little less impressive considering they were run on fast tracks that saw quite a few track records fall over the course of those weeks (CD, for sure).