Undeniably a "made-up PR term"--but sometimes they end up being "sticky" because they're undeniably compelling. In this case, no matter how cynical/base its origins might have been, "Ladder District" really works in that it keys people in to an interesting geographic suboddity within greater Downtown Crossing--that actual "H"-alignment of all those streets.
Think of explaining to a little kid while pointing to a map, "and that's the Ladder District. See? Because the streets form a Ladder." "Neat!"
Everything in this world was invented at some point--authenticity is always contested terrain. In the marketplace of ideas, I think "Ladder District" has succeeded for all the right reasons, whereas coinages that are truly grotesque--"SoBo"--continue to be laughable, and for good reason.