Okay, to start with, I'm not a paramedic or a doctor, I'm a First Aid Instructor.

I would say, follow your first aid training, or treat to whatever level you have been trained to. Depending on the location, and how long they expected to take, I would probably not bother with a splint unless I planned to transport the casualty myself, and I would only do that if it was a minor break (a broken arm, wrist, or ankle, possibly a lower leg or knee fracture) and then probably only if it was a friend or relative.

Under no circumstances would I move a casualty, especially a pedestrian struck by a car, unless there was absolutely no other way to ensure their safety. The number of people who are killed every year by well-meaning bystanders who "move them to safety" is something I prefer not to contemplate. Without an X-ray machine or similar apparatus, I doubt you're qualified to make a judgement as to whether there are spinal injuries, and there could well be other non-spinal but life-threatening internal injuries that could be aggravated by moving them.

Your three priorities in First Aid, in order, are:

1. Preserve life.
2. Prevent further injury.
3. Promote healing and recovery.

If you have a pedestrian hit by a car, with the attendant possible life-threatening plus head and/or spinal injuries, I strongly suspect that the ambulance will be there before you can even start to splint a broken bone.

However, in the event that you have gone through your scene survey and your primary survey and have treated any obvious life-threatening injuries, and the paramedics are still stuck in traffic or whatever, then I would say (as a First Aid instructor), to hell with what the paramedics "want", do what you've been trained to do. If you have a triangular bandage in your FAK, go ahead and put a sling on that broken clavicle. Put a dressing on that cut and tape or bandage it in place. The paramedics will probably whip out their shears and remove it when they arrive, because they have an obligation to examine the injury themselves; that doesn't mean you were wrong. Making the patient as comfortable as possible before the ambulance arrives, even if it's only for 30 seconds, is not something to be dismissed.