I can tell you after a rather scary experience in September fishing in the JAX area, one can be shot down if they are within 1,000 yards of any active duty ship.
We found out after our fishing guide took his boat and 3 of us within 100 yards of the JFK. Within minutes we were staring at a cocked and ready 50 caliber gun on the front of a Coastie boat.
That was when we found out about the current 1,000 yard limit.
I can tell you from being in the Navy in the Jax area, that you aren't going to get shot down instantly for coming within 1000 yards. Flyovers in international water cannot be stopped, except if by an act of war.
100 yards to any large ship is TOO close. To a warship it is threatening and you will have weapons trained on you, as you did.