Disclaimer: It's been around 25 years, but I was an athletic trainer in college and based on the initial actions of the training staff, you can almost immediately cross off a ruptured Achilles. A fully ruptured Achilles is unmistakably obvious and would look like a softball rolled up in his calf.
My guess is he has a grade 1 or 2 calf strain. Now that does involve partial tears more than likely, but I think they (the medical staff and O.J. himself) thought that it was merely a bad cramp (possibly wishful thinking) initially.
Just my two cents