Ground control wouldn't have cleared them to hold short, or to position and hold (US: "line up and wait"). That would have been the tower, not ground. Ground is only responsible for taxiways, not runways.
The Coastguard plane was cleared to hold short at C2, but entered the runway instead from C2 as if cleared to position and hold (Edit: Or maybe they thought they were cleared to take off, but that's far less likely).
Because I think you'd appreciate it, and no pedantry intended: "Line up and wait" is the international terminology, which the US was relatively late to adopt.
