Question:
About 9 months after I started driving, I found myself in a situation.
I was on the 285 Loop going around Atlanta. Haz-mat (forget which kind, but does it matter?) was in the box. Placards all around. Back-up was horrible - much worse than usual. I was in the right lane of 4 lanes total when I oozed around a corner. A car fire was in progress on the right shoulder about 200 yards ahead. No fire truck in site. Haz-mat rules say no open fire allowed within 50'.
What do I do?
The far left lane - 3 full lanes at 12' wide plus another 2'-4'- would put me well within the 50' zone. (And besides, trucks are forbidden in the left two lanes.) Pull off on the shoulder, put out my triangles and wait until it's over? (Is this an emergency?)
What I did was put my left signal on to move over. No one gave way. I'm idling forward. Nobody would yield. After time and almost half the distance was chewed up, I did the 'ol slide to the left and give them a choice of giving me the lane or having a physical confrontation. Second lane over was mine.
With signal still on, I did the left fade again to gain the third lane. These people were bold. No yield. Nobody.
I passed the car fire with my haz-mat filled trailer about 15' away.
What would you have done?

Answer:
Here are a couple of options and thoughts:
What was the haz-mat? Flammable, corrosive, etc...?
1. You might pull over safely on the shoulder AT LEAST 50 feet from the accident, put on your flashers and lay out triangles, wait until the fire department arrives and wait until the fire is contained to pass. If someone asks why you are there, show them the bills and explain the situation. An official might safely direct your rig around the accident. This is the Cover Your Assets approach.
2. Another option is when you first found yourself in the backup, you might have gotten on the CB to find out from other drivers what the accident was and at what milepost. Knowing you have haz-mat, you might have been able to find an alternate route safely around the accdent and back to the highway. But, you want to be careful not to get into a residential area, so this plan might have involved using the exit to go back around the 285 in the other direction. Now haz-mat transport requires a planned route, but in cases of emergencies, routes must be altered from time to time to ensure the safety of the load.
3. You can get in a lane as far from the accident as possible and pass it, but that's gambling for sure.
Just some ideas. Maybe your company also has input on such a situation. You can never play it too safe when it comes to hazardous materials.

Answer:
Those rules pertain to parked vehicles, not to moving vehicles. Seriously, you could have a "fire" in the heater of a horse carrier passing you. What about a fireplace in a house next to the road? What if somebody is cooking on the gas stove in the RV driving down the next lane?
I think you are reading too far into the rule. If it were a large roadside forest fire, though, you might consider stopping, but even then, the fire might eventually get you.
Answer:
Slightly different rules apply to different classes of HazMat. Explosives, flammable and combustionable classes are generally where the rules pertaining to smoking and fires pertain.
So the answer to your question would depend on what you had in the trailer.
Answer:
Here's the safe way to view it:
If you had hazmat....especially "Flammable" material that required placards, you should have stopped as soon as you saw the burning vehicle.
If a car is on fire...there is no guarantee that the fire won't reach the fuel tank and cause it to explode, vent, or just burst and dump its fuel on the road. Oh, I know, it very rarely happens....but what if just this once....as you are passing by...it does pop(!!)...and a piece of flaming debris punctures your trailer, and ignites your "Flammable" freight . You are now in a real pickle. If your trailer explodes... you are most likely dead, and many others too. And if you should survive, the resulting legal problems that follow may well make you wish you were dead. Just plain too risky. I would have stopped, messaged the company, and told them I was shutting down until the fire was out.
Secondly....if some "junior jackbooted quasi-nazi skinheaded recent academy graduate" saw you pass the fire close enough to violate the rules.....well, you know how thats going to end up...right??
Remember....discretion is the better part of valor.So I like what I do, you don't, too bad, get over it. Get on with your life, I am.

Answer:
I was pulling a load of flammable paint UN1263 and had the hub on the left front tire catch fire. I pulled over and started to fighting the fire. I had a hell of a time getting it put out and was just about ready to pull the pin and pull the tractor out from under the trailer, no landing gear or anything, and then I finally got the flames to stay out. Super scary! But with HAZ-MAt you have to be thinking ahead and be proactive.
I am now a full time fire fighter and my informed opinion is that you should have stopped! As far away as possible and hopefully upwind. I agree with Skywalker on that. What you have in the box does matter but regulated material is regulated material... the rules are the same. A fire scene is bad enough but you DO NOT want to be involved in a HAZ-MAT incident!
Just my two cents...I am certified as a HAZ-MAT TECH which means that I am trained to the level that I can donn a fully encapsulted level "A" suit and actually go in to the hot zone and try to stop a leak or mitigate whatever situation is at hand.