A point to make in pushing the vehicle out of the way. If that's faster and safer, that's what will happen. But have you noticed how shiny and nice looking fire equipment usually is? That's because its (1) life saving equipment(2) owned by the citizens of the county or city(3) and VERY expensive.
If its a choice as to an illegally parked car getting broken windows or the fire apparatus getting dinged up, the car is going to lose.
Sometimes you can work around the car, mostly you can't due to aforementioned kinks and time involved.
In summation, that car will have the least priority at an active fire.