At least not in the truest sense. It is airborne in lab settings when in AEROSOL form. Not in a real world setting. So unless they were doing a lot of procedures that create aerosol (like drilling teeth) in those nursing homes, it wasn't spread that way. Not gonna travel through an HVAC system or linger in the air for hours from a cough or sneeze.
Obviously, I'm no Epidemiologist and that is all second hand.
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This guy produces videos about this every day. I think he is credible. He summarizes a recent study that says the virus can survive for three days on surfaces and three hours in aerosol from sneezes/coughs, etc.
Link: https://youtu.be/JNQUHc8wbRc
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in limiting transmission, it would be on disinfecting surfaces and social distancing.