I'd say its "taking the high road"..something good leadership does. Their beef isn't with the kid so no reason to shame him over his fathers childish behavior. That's just my take though. Even if his kid didn't apply Harvard did something, perceived or real, to Trump which is why he is going after him. If you look at every aggressive over the top thing Trump does its always in retaliation for "something they" did to him. Always.
But my point is the rumor gets out there and the White House has to release a statement about it just reeks of desperation and comes of to me as a sad attempt to cover up the truth. Trump knows he can do pretty much anything and not be personally held liable as President. What he doesn't understand is that there are still consequences for his actions and the spin doctors gotta act fast to try and smokescreen his buffoonery.