Okay, let's forget empathy. The problem with pointing it out, logically, is that it is a complete waste of time and energy. The athlete is already aware of his medal status. If he feels that he let his father down, then he already knows that, as well. Pointing either of those things out serves no logical purpose at all; the only likely effect is to make the athlete feel worse, which does not change the outcome and is unlikely to improve future performance.
In short: if you truly do not (or cannot) care what other people are feeling, then perhaps there is nothing wrong with doing it, but no reason that you would. If you would send such a message, then you do care; that's why you're doing it.
Applying your standards to others' actions, and vice-versa, simply does not work; surely you learned this long ago.