Now depending on the issue it is faster to drive/be driven from where I work so an ambulance is often not that useful. For example a while back a coworker ate a tamale off the food truck only to find out that it contained peanuts. After noticing the reaction the owner took him to the ER personally (Coworker used his epipen as soon as it was known he needed it.) It is ~8 mins by car and at best an ambulance would have been 6 here and 6 back for an arrival time of 12 minutes. Now had they not been breathing they probably could have gotten a fire truck here in 2-3 mins to administer some epinephrine but they would still have had to wait the same 12 minutes to make it to the hospital because the fire truck EMT's can only do on site treatment.
So unless it is extremely dire taking a coworker to the hospital can be faster than an ambulance. That said a crushed hand or cut off finger? That is one of those where seconds matter and the fire truck/ambulance combo would be used.