You get involved immediately because it's the right thing to do. Waiting could risk the victim sustaining a serious or fatal injury.
IOW: do the right thing, dammit.
Again, that's easy to say when you're not in those situations. Waiting could also avoid you and others sustaining a serious or fatal injury. The two instances aren't the only ones where ordinary citizens have died trying to help someone they thought needed it. Those are just two of the ones that were a little closer to home. If that had been any of us trying to help in those situations, we would be dead too. Sure you'd be eulogized as someone who was trying to do the right thing, someone who simply wanted to help as they were, but you'd still be dead.
As I said, it's a fine line. You don't just run around town drawing a gun on people when you think it may be necessary. You also don't just jump head first into every volatile situation you come across.
Another story in a different vein (I got a million of 'em). I was coming from a Cowboy game one Sunday night and as we walked to our cars we could hear someone revving the heck outta their engine. It was a Volkswagen beetle with aftermarket exhaust and all that jazz. The tires screeched as they raced outta the lot.
I hit the on ramp to get onto the highway. This is single lane with a decline and a sloping, grassy embankment. I hear the revving engine again and look in the rearview of my car to see that same Beetle that had left the parking lot before I did. Mind you, I have two people's kids in my car and another adult.
The driver of the Beetle, who I would later find out was a 20 year old girl, decides I'm getting on too slow and tries to go around me. As I said, this is a single lane on ramp, so both cars can't fit. The Beetle is beside me. I could've literally reached out and touched the other car. I had no room on the right to move as there was a curb and I didn't want to hit the brakes as there were other cars behind us. Well, she runs out of road and careens down the embankment throwing grass, rocks, and dust back upon the car I was driving.
The Beetle slams into the concrete base of a light pole, goes airborne for about 30 feet before coming down on its side, sliding to a stop and bursting into flames.
At this point I'm furious. I'm furious that this idiot just endangered not only their lives, but the lives of myself and everyone in the car with me. I was so mad that I almost kept driving. But, I couldn't do it. I couldn't let people possibly die knowing I may have been able to save them.
I pulled off of the bottom of the ramp where a median was, grabbed a cooler we had taken to the game that was full of water, and raced to the car. I dumped it on the fire and several other cars began stopping and coming over to help put the fire out. There was blood everywhere. The girl was stuck under the steering wheel screaming and the guy with her was unconscious. Both of them lived by the way.
But, I said that to say this. I ran to help them, yes, because it was the right thing to do. I ignored my anger, and the raging flames to try and save someone. Could I have been burned or run over by a passing car and killed? Sure. Did I think about that at the time? No. Each circumstance is different and this is waaay too long of a post. Fine line.