Well, I remember my buddy pointing it out to me after Secretariat had been a favorite up there, but not seeing it before. If ml/nj and I are incorrect, I know I am surprise and so is he!
Bottom line is when was the spring built, and when was it named (which may be different). If they are before 1973, unquestionably it was meant for MOW (speaking of legends/favorites at Saratoga - MOW ran 4x at 2yo and 2x at 3yo as well as being purchased there, where Sec ran 3x and once, respectively).
Unless that spring is very young, I’m guessing as his pet name was co-opted from MOW, honoring Sec was tacked onto what already existed. I’ll bet the track people decided they’d include Sec in the honoring after the fact since he was seen as such a superhorse having the same pet name.
Phar Lap is the other well-known “Big Red”, 10 years after MOW.