There is no reason to go for engine shutdown = rotor shutdown for on board refuel, a rotors running refuel is no more hazardous than HIFR.
Spoken like a land-based pilot.
That all depends on things like the refueling point(s) on the aircraft and sea state.
If one assumes that a HIFR-capable aircraft is also fitted with a single-point pressure fitting for ground refueling, that renders the first point moot, so we'll dispense with that.
However, if the aircraft is not HIFR-capable and the ship is rolling beyond a certain point and / or needs to maneuver during the fueling, rotors running on deck is WAY more hazardous than a shutdown and takes longer than HIFR. Also, most naval regulations require the use of a single point pressure fitting for hot refueling, at least it used to be that way in NATO. Training is important for HIFR, as anywhere up to 30m of hose is suspended from the aircraft's winch hook and oscillating between the ship and the aircraft, and that hose is full of nice heavy fuel.
At least in the U.S. of A., Army aircraft refueling systems are designed for 15 psig (about 1 BAR) and those of Naval aircraft are designed for 55 psig. So, sometimes a shutdown simply has to happen.