My uncle worked for a place where a vendor CE had a heart attack and died in the early morning in a raised floor space control room. Someone called 911 multiple times and due to bureaucratic fuckery security didn't let the EMS in multiple times. In short, the dead guy was wheeled back and forth by operators for 12 hours, when the plant manager dropped in and lost his shit and took care of it.
Like I said somewhere else, this topic is a corner of the world that sounds insane if you're not in it.
Where I work, 911 has no idea where we are for reasons, and a serious incident where a person isn't vocal requires a floor sweep. The emergency services don't have the time or interest to handle your company's internal stuff, particularly if you have a high call volume.
Unless there is uncontrolled bleeding that is definitely not a "seconds matter" situation. Sure, you want to get to a surgeon sooner rather than later, but an extra 5 minutes isn't going to matter.
Where do you even begin to make that sort of claim?
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.