I would suggest the 'side to side' vibration was ground resonance rather than dynamic rollover.
The report did not indicate that the aircraft was chained / chocked to the deck, which is why I didn't think of that as an issue. But I suppose that there are a variety of ways to enter ground resonance.
Beyond that I won't go - if they landed, got into ground resonance, and didn't lift back off right away I can see the point you are making.
But I am guessing again here.
I don't remember how badly the lateral vibes get when the main rotor dampers leak all of their fluid out, but I do not recall that particular mechanical failure being taught to us as so severe that it makes the aircraft unflyable. Perhaps John Dixson may be able to shed some light on that if he drops by).
There's another possible scenario that occurred to me during lunch.
A few hears ago a UH-60L (from which the CH-60S => MH-60S is directly descended) had a considerable length the skin (aft of the spar) on a main rotor blade come off in flight. The aircraft got a heavy vibration, the crew did an autorotation, and they reported very heavy vibes at the bottom when they cushioned the landing at the end. (All walked away).
That offers me another possible scenario as I think through that very sparse report: what got that observed lateral behavior started?
If, as they approached the ship, a similar blade skin dis-bond happened, severe vibes would show up since they still had power on. Again, the lack of detail leaves this as "a guess" ... I suspect that it will be a while before more is known as the investigation has begun in earnest.
Thanks for sharing your thoughts, crab.