Yes it is a bug. If you own classic and not Reforged the BattleNet application does not allow you to install Warcraft III when online despite you having a licence to play it. The work around, as you mentioned, is to open the application in offline mode and install from there.
last I checked the BattleNet application allows you to install any game when in offline mode, even ones you might not own. However in order to play the game you will need to login during which time the licence check is performed and the game will refuse to be playable without a licence. This works for StarCraft II, Diablo III, e.t.c.