Did you mean this street https://www.openstreetmap.org/way/130764273 ? Please have a look on the value tiger:zip_left = 20001 and tiger:zip_right = 20009.
Only the houses on the right have a zip code (addr:postcode=20001). The street above (Hobart Place North, https://www.openstreetmap.org/way/6056624)) and below (Gresham Place Northwest, https://www.openstreetmap.org/way/6054391)) have booth the zip_%=20001. It seems better to me to correct the errors in the data than to correct the results of nominatim. But I myself do not have sufficient knowledge of the local conditions.