Unless he's under contract of some sort including union, then yes, he can be terminated. It's BS in this case, but it is what it is.
The problem is even if he did fight and got his job back, chances are they would just get rid of him later for no reason, and they don't need it.
On the other hand, if the guy that fell wasn't moving, then your father probably should have just called for help and waited. This brings to mind something from working at the airport (although on a different scale.) If a plane crashes on the runway, we as the airline employees are not allowed to go out on the runway and assist. We have to wait for help. So in your dad's case, unless the guy that fell absolutely needed immediate assistance, there's nothing your dad could have done.