How "secret" is getting a dragon kill supposed to be?
When you see an enemy champion kill the dragon, there's a whoosh sound, a particle effect around each enemy champion, the countdown resets on the scoreboard, the icon on the scoreboard changes, each enemy champion gets a buff, and there's a chat message. If you don't see the enemy champion kill the dragon, all of the above happens, except the countdown doesn't reset and there is no chat message. Why? You make no attempt to hide the fact that they got a dragon kill; you still hear the sound effect, see the particles, and see the buff appear on each enemy champion. And yet the countdown at the top of the scoreboard continues to hide exactly when the dragon was slain.
The entire point of the jungle camp respawn timers was that it was decided that, of all the skills Riot wants to foster in their players, note-taking is not one of them. Players shouldn't have to keep track of any more long-term information then they need to. By not making the dragon timer public information when it's already available to the players, you're just adding unneeded complications. Either hide the information or don't.