As far as I know if you have done something that could be serious they would far prefer you to err on the side of caution.
It is also better safe than sorry as after an accident you are pumped through with adrenaline. I have walked into A&E with what I thought was a minor set of grazes and been told to sit down, not put any weight on my legs and not move until they can get me an x-ray as it was possible that I had broken my kneecaps. I hadn’t, but I am not really qualified to make decision as to if my inquiry is potentially serious or not.
If it looks like someone might need one. Call it.
EDIT:
To add to this I know someone who broke their ankle walking in some hills (quick close to a major road). They sent two emergency vehicles (ambulance and fast response) because “It is possible the fast response could get their first, but we don’t know so we are sending both”. Turns out that you can cut off blood flow and if it isn’t sorted quickly you can loose your foot or something. In other words something that I didn’t think was quite that time critical was.