the bill submitted for the damages to buildings, vehicles, lightpoles, sidewalks, houses, streets, etc... because often-times these fights take place or start in or end in a city, the ravages of battle can take a very real toll upon those things, and it's not like cities typically budget for "superhero/villain damages" due to x-number of fights per year, so we'll budget x-amount of dollars in anticipation of those rumbles happening. Someone has to foot the bill for all those repairs. I bet the cost of insurance in places where superhero's rumble the most has GOT to be exhorbitant, and only the extremely rich can actually afford it.
I believe it is a combination of a UN fund for any group calling themselves the Justice League of America and a specific fund created by Bruce Wayne and Ollie Queen that allocate funds for damages that have resulted in battles with the JLA and others. The UN still sanctions JLA activity, which is why they still have problems operating outside of UN jurisdiction. The only difference between now and the previous JLI is that they do not answer directly to the UN, nor are members salaried or have embassies around the world.