One Wednesday morning last winter, a big evergreen-colored garbage truck from Bowie’s, Inc. lumbers into the parking lot behind Politics & Prose bookstore. The sound of its engine breaks the quiet as its mechanical arms grab hold of the Dumpster and unload its trash into the back—a tumble of black plastic bags filled with coffee grinds, food scraps, greasy takeout containers, and castoff paper products.

After the truck releases the Dumpster, the garbagemen get their hands on something that doesn’t mix well with all that rotting garbage: the recycling. They roll up with bins holding newspaper, cardboard, bottles, and cans—all dutifully separated by employees at the bookstore and other businesses on this upper Connecticut Avenue strip. One by one, the men tip the contents of the recycling containers on top of the refuse—the bottles make a tinkling sound as the glass shatters against the truck bed.

Then: They go back to collecting trash. The driver hits a switch and it’s all smashed together before disappearing into the belly of the truck.

An exception? A rare case of wrongful commingling?

It doesn’t look that way if you spend some time following trucks of various private garbage companies around town. D.C. law requires recycling at all city buildings, though the law appears to stop at the threshold of all alleys. There, behind businesses and apartment complexes all across the city, this sloppy ritual goes down with striking regularity: In a blur of asses and elbows, workers throw stuff from green containers, black containers, and blue containers in the same truck, creating a jumble of trash and recycling that can never be de-mingled....