The controller told the truck to proceed, before telling it to stop. That was a serious ATC error.
Controller probably should've told them to expedite the crossing or warned that traffic was about to land, but they were managing a lot at once; tower+ground by themselves and an emergency already.
Doing it at LaGuardia or any major airport is absolutely nuts.
Add a few seconds for human reaction time on both ends, I don't think that's really "enough time to cross safely" - maybe if the stars align.