Well apparently this is normal operation of the range. I was very dubious of this but I talked to the guy and he showed me exactly what was happening and that there was nothing he could repair/adjust/fix to make it act differently.
Basically, when the oven door opens it creates a suction in the air channels that the burners need to get the air they need. Generally, this is only noticed when the flame is on the lowest setting (which it was) and it typically goes down but comes back on. We replicated this many times. He could not explain why the flame went completely out nor could we replicate the flame going completely out and not coming back on. His guess was that a pot being on the stove, the oven going and the burner being on the lowest setting all came into play for a bit of a worse case scenario add to that maybe some wind from the window being open came into play.
Of course this is not too comforting, but a stove, like other things in life deserve and require a certain level of respect and I guess this condition is just something we have to be aware of and take steps to know when it happens. Basically, something to be aware of. Between the gas company and the repair person, I'm confident that I don't have a gas leak. But, we did create the conditions that allowed for a gas escape.
I'm also concerned that my gas detector, which is right next to the stove, did not go off. I don't really have a way to test it so I guess I'll get another one just to try to be sure.