Interesting thread. I've worked for private companies only, one providing 911 services with the fire department (a horrible arrangement, don't get me started on that) and another that ran IFT and had contracts with nursing facilities. They would call us instead of 911, because just about anytime you call 911 here, you get a rig, an engine, and at least one LEO. They all usually come in hot, are loud, and would disrupt the (often senile and easily agitated) residents.
For the 911 service, we ran hot to everything except SWAT standbys. Kind of pointless, in my opinion, as fire there thought they were gods, and although we were ALS, fire had medical and scene control - it was rare they wouldn't have at least one fire ride back in on everything. They probably would be better staffed with a single EMT driving the rig, that way the EMT couldn't point out that it might be a good idea to get a 12 lead and a line before giving nitro, but I digress... Emergent returns were at the discretion of the attending provider, no protocols for required C3 returns.
For the private service, dispatch (without the aid of computers or cards) would decide response priority. More often than not, we came in non-emergent. Since we had contracts all over the greater metro area, sometimes we would run hot simply because we were greater than 10 miles away and the nursing facilities around here are not known for their good medical judgment. The owners of the company would also play fast and loose with these rules, sometimes just to impress a facility or client, we would be told to step it up to get to a hospital discharge; or the one time a BLS crew didn't call in for a refusal - they were told to run hot back to the scene to get the doc a piece of information they had forgotten. As far as emergent returns, company policy dictated that they were at the attending provider's discretion, however after determining exactly once that an emergent return was warranted (craziest thing, patient exhibited contralateral decorticate/decerabrate posturing and a severely altered LOC, my partner and I were like quad the :censored::censored::censored::censored

due to the fact that it was rush hour and shortened our transport time from about 30 to 12 minutes, the company, for their own reasons, used it to discipline me. Essentially what I'm getting at is while they had a decent system for response priorities (depending on who was dispatching), they only played lip service to what was written in their handbook.