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Laurence:  First, there is a problem with your methodology.  You are comparing the net change in households with the net change in car-free households.  That gives you absolutely no information about the number of new households that are car free.  You recognize a critical assumption that no existing car-owning households went car-free, but you haven't recognized your implicit assumptions about the percentage of departing households that are car-free, and the number of departing and arriving households, or other factors such as household formation, or the what percentage of the total number of households is departing or arriving.  I don't know if ACS has tables with the information that you would need to isolate vehicle ownership by new residents, but there is no reason to believe that the Census data supports the claim that 45% of new households are car-free.

At any rate the information on historic vehicle ownership rates that was posted at the link you provided sheds light on the longer term story:

"We might want to look at some more reliable Census data:

1990: 37.4% of DC households were carless (based on Census long form);

2000: 36.9% of DC households were carless (based on Census long form);

2012: 36.5% if DC households were carless (based on 5 yr ACS data, since Census long form was abandoned in 2010)."