I'm not following this whole line of thought here.
The cruise ship will NOT BILL YOUR INSURANCE, period, they do not do that.
If they did not give you any sort of bill, then my guess is that they are assuming they were at fault somehow, and the free treatment was a gesture of goodwill. (See my previous post.)
Again, this is NOT ODD for a cruise line medical facility, they do not always bill the passenger for services.
And honestly, some medical insurance policies won't even cover you for what happens on a ship.
Travel insurance will usually pick up what your personal medical won't cover if you have all the documentation and your policy covers medical expenses.
Regardless, as the parent of a 17-year-old myself...I hope your son recovers well and there is no scar from the accident.