@MS great question. The answer re public water is it depends on the scenario and the type of public waterway(ie interstate lake or river, navigable waterway, landlocked lake etc) and the type of public entity involved. It also frankly depends on The nature of the activity and quite frequently nature and level of the insurance involved.
But I think you hit the nail on the head re other's people's money. If you are unlucky enough to be sued as a boater, lakeowner, homeowner, car operator, etc., if you are properly insured your insurance carrier should pay for your defense in most lawsuits and indemnify you(pay any judgment or settlement).
Without insurance, you are on your own... Which is not good
Gotta love America....you can sue anybody for anything at anytime. It does not mean you will win, but your insurance premium is worth the piece of mind....