> Occam’s razor requires us to consider the possibility they just had a really good, well timed dosage of performance enhancing drugs for Secretariat back in the day.

No, Occam's Razor suggests the simplest possible explanation. To suggest that they figured out how to dope horses in 1973 and then promptly forgot how for the next fifty years is a complicated explanation. The simplest explanation, the Occam's Razor explanation, would just be that it was a fluke of nature.