No, you wouldn't... or at least I hope you wouldn't. The right answer is "we would use common sense". If you're running on the 4th fire alarm at the same location and there's a rollover accident in the intersection with multiple ejections, you would stop. If it's a 2-car fender-bender and you're running on a structure with people trapped, you continue on. If you're involved in the wreck, either directly or as a causative factor/non-contact vehicle, you stop.
In this case, the DE did right by stopping. They went off-road and were concerned about damage to the apparatus, and they likely weren't sure if they made contact with the idiot's vehicle or not. It's just a shame there wasn't any LEO following them. Several of our deputies/troopers like to follow us when possible on calls... when we get people failing to yield or otherwise acting moronically, they are in a great position to stop and have a chat with the offender. Maybe even give them some paperwork to remember their poor behavior by.
And, to respond to the OP, in 6 years of volunteer service and over 1,000 runs driving I've had:
1 wreck - a driver who was most likely under the influence (hasn't been to trial yet, felony warrant issued for DWI 3rd) struck us while blocking traffic on a highway. $55K of damage to an F-750 medium duty rescue.
1 near miss - 4 teenagers in a small car pulled out in front of me from a side street while returning from a call in our 1250/2000 tanker/pumper. Between the air horns, liberal application of the brakes (nothing like feeling 38,000lbs. sliding around), and some aggressive steering I was able to miss them. Had they been any slower, I would have impacted the front passenger door... I don't really like thinking about what would have happened in that instance, but it wouldn't have been good.
And, of course, various other things torn up. Scratches on brush trucks, a few flat tires, a damaged extension ladder (backed into a tree - pedals were very close together and my hoof got both simultaneously - d'oh!), etc.