I don't think the ATC instruction was as clear as it could/should have been.
A bit of British Understatement if I ever heard it!
When ever did you describe a "departing" or "Learjet departing" or even "traffic on the runway" as "rolling OFF the runway"?
That being said.....when crossing down range of a place where speeding bullets fly.....it behooves one to keep a sharp eye out the window. There is no excuse for not seeing an aircraft taking off from a runway no matter the color or size even in the dark.....as they do have lights on.
Is that not why crossing at mid-field is usually the best practice?
You pass over them fixed wingers while they are still ground bound as they launch or land. It sure cuts down on the possibility of meeting one in the worst way.