That is a good point but it seems instructions for ground vehicles seem to really stress this. For example this one:
https://skybrary.aero/sites/default/files/bookshelf/1003.pdf

Says at pag 9:

"While driving on an aerodrome : Clear left, ahead, above and right

Scan the full length of the runway and the approaches for possible landing aircraft before entering or crossing any runway, even if you have received a clearance."

I am afraid the fire truck might have some level of responsibility, since it seems FAA ground vehicle guidance says:

AC No: 150/5210-20A - "Subject: Ground Vehicle Operations to include Taxiing or Towing an Aircraft on Airports"

https://www.faa.gov/documentLibrary/media/Advisory_Circular/...

“you must ensure that you look both ways down the runway to visually acquire aircraft landing or departing even if you have a clearance to cross.”

These trucks seem to have pretty good visibility from inside. Not sure if La Guardia model was the same: https://youtu.be/rfILwYo3sXc

Hopefully some commercial professional pilots will comment on this thread, but if you go to sites where they normally hang out like:

https://www.airlinepilotforums.com

You will see many are terrified ( in commercial pilot terms...) of flying into La Guardia or JFK...