Flint is an example of an acidic water source leaching lead from supply lines into the consumers' water supply. Not an inability of the waste water processing facility to clean the waste and contaminants from flushing toilets.
With wet cleaning, it is all captured in the water and goes down the drain. Municipal water stations can clean it out of the water before releasing it into the environment. This option i consider the best.
If you are on a septic system, then it all goes into the dirt at your house. Also, if you clean and rinse outdoors, it all goes into the dirt, too. Then, leaches down into the groundwater supply. These options I consider bad.
Dry tumbling puts the lead into the media. Some media dust will, over time, migrate to the areas around where the the vibratory tumbler is operated. This dust can spread around the house or garage. Then, when you change out the media, it all goes to the land fill. Landfills have some mitigation to prevent leaching into the ground water supply.
YMMV or in other words... Pick your poison, I guess. However you choose to clean your brass, the lead residue ends up somewhere.