Ezra, I don't think Obama specified which Rocky-Apollo fight he was referring to. Given that Obama identifies as Rocky, we can probably assume he means the fight Rocky won, in Rocky II. In any case, he wasn't referring to the outcome of the match, as much as to the hype around it, and how that sort of thing can distract from the important issues under discussion, or, to continue the Rocky analogy, from the rustic, unadorned beauty of two human beings beating each other to a permanently brain-damaged pulp.
In regard to Obama's use of the reference, I would offer that, despite being released all the way back in 1976, some awareness of the first Rocky, its plot, central characters and themes, and its contribution of the "training montage set to orchestral funk guitar solo" to the American filmic vocabulary, falls under the heading of "basic pop-cultural literacy." I am interested to hear others' opinions on this.