Could you shed some light on this?
Murder in the White House
Murder on the White House.
What's the difference?
One more question:
if we say 'on' the White House based on the fact that we don't know precisely where the incident happened...would it be wrong if it (had) happened inside the building?
No, you would say "on the White House" if it happened on the roof!
You'd say "at the White House" if it happened in or near the White House, somewhere on the White House grounds. It doesn't have to be inside, but it could have been.
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.