Er, No
At least in large commercial and apartment buildings, burning "bunker fuel", that is heating oil #4 and #6 is still allowed. Our building burns the former, while many UES and UWS buildings burn one or the other.
Will grant you that for one to four family residential homes, #2 is the only fuel oil allowed, unless perhaps one has some sort of grandfathered burner etc...
Large commercial buildings in normally obtain natural gas under a system which allows supply to be stopped should demand increase elsewhere. In which case the burner would have to switch to another fuel or not burn at all.
Other buildingss, simply by virtue of being around so long (think those stately old co-ops on Fifth, Park Avenue, and Central Park West), at first burnt coal, then switched over to oil.
Numbers four and six heating oil are basically one step away from tar. The stuff is so thick it must be heated to move freely and kept circulated in the tank. This fuel is also quite dirty to burn, which accounts for the soot that covers many NYC/Manhattan areas. My window sills and windows are black within a few weeks (if that) after cleaning, because of this soot.
Building owners like #4 and #6 (especially) because it is cheap, very cheap. These fuels are much cheaper than say #2 (residential fuel oil), but natural gas may be cheaper than any of the oils. However there are huge costs in converting to gas that may take years to recoup.
Finally as for homes burning oil in the Northeast; many home owners simply refuse to convert to natural gas, thinking oil is alwasy cheaper. Also many people still believe that natural gas can lead to one's house exploding.
In some areas of the Northeast one has no choice but to burn oil as there aren't natural gas pipelines close, and or pipelines down one's street. The cost of bringing gas to one's home if the pipe runs down the street is dear, but doable. However when you start talking about bringing gas into an area which does not have service, it is probably more than it's worth for both the consumer and gas company. Only way around would be if enough homes and or businesses signed on.