I think he means that he stated the result in a calc class, not that he proved it. It would be very reasonable (and cool!) to state without proof in a calc class.
I certainly won't presume to tell Will Stein about number theory, but it seems strange to me to include in a calculus class (even without proof). Far be it from me to suggest ever excluding interesting mathematical content, but I'd be suspicious of an ordinary calculus class appreciating the significance of this result. On the other hand, maybe such prophecies are self fulfilling, and the enthusiasm of the teacher engenders the enthusiasm of his or her students, whatever the material.
(I am curious what "the resulting corollaries" are, though.)
Hmm, well you can read for yourself, my prof is nice enough to have posted all of the lecture notes online;
These are the lectures from the second class where the result is covered on the third page:
To be clear, I didn't mean "Are you joking?" as in "You are obviously lying or mistaken"; I really meant, exactly and only, "Are you joking?", because I found it incredible. Well, obviously you are not; and I would have taken you at your word without proof, but thank you for the careful documentation.
I still would be hesitant to talk about this in my own calculus courses, but, given the impression that this made on you and Will Stein's endorsement (https://news.ycombinator.com/item?id=12886751), it sounds like that's just undue timidity on my part.