I would say that there are simply not enough ambulances in D.C.
According to wikipedia (I'm not motivated to look elsewhere; I just needed some quick figures), D.C. has a population of 632k, and they have 39 ambulances, 14 ALS and 25 BLS. For comparison, in Fairfax County where I work, which has a population of 1.1 million, we have 41 ambulances, all of which are ALS, and occasional volunteer participation, which can add a few more BLS ambulances at any given time.
Both Fairfax and D.C. have transient populations every day, workers, tourists, and people passing through. Even though the number of ambulances is almost the same, Fairfax is very affluent, with a relatively young population, so people aren't generally chronically ill to begin with, there is very little gang violence or other traumas, and the residents are more apt to actually drive themselves to the hospital, rather than call for a cabulance. In D.C. there are much older, poorer residents in poor health, and people of lower socioeconomic status are much more apt to call 911 for very minor/chronic issues that are inappropriate for 911 EMS transport (the proverbial toe pain, so to speak). A busy 24 hour shift for a Fairfax unit would be 8 calls, maybe ten, and most units fall well short of that (probably 3-5 calls a day on average). In D.C. I'm sure that they're on the road constantly.
Let's do an apples to apples comparison - D.C. to NYC, two urban areas with a significant portion of their population being of low socioeconomic status. NYC has a population of 8.3 million, and has 624 scheduled ambulance tours (212 ALS/412 BLS). That's one ambulance per 13,301 people. For D.C. that's one ambulance per 16,213 people. It's clear that D.C. is operating with 20% less ambulances than NYC, per capita. I used to work in NYC 911 EMS (NS-LIJ Hospital), from 2003-2007. I can't recall even one time that the police of fire suppression needed to txp a patient to a hospital, due to no ambulances being available.