Several years ago, when I worked for a living as a Collision Investigator, we attended a double fatal collision involving a caravan with a punctured tyre. The circumstances were that the offside tyre had punctured, and so they driver stopped in the nearside lane of a dual-carriageway road (as far over to the left as possible), and started to prepare to change that wheel. His wife was stood between the car and caravan seemingly keeping an eye out for him and possibly believing that the caravan would provide some protection.
The traffic was generally passing by without any trouble, but along comes 44 tonnes of artic and drives through the lot, killing both people in the process. The cars behind the artic had seen the caravan and moved over to the offside line, and couldn't believe that the truck didn't move over too. On the morning, it was slightly misty, but there was still at least a quarter of a mile view (and the caravan was in view for that length). The truck driver was convicted of Causing death by Dangerous Driving x 2, but that will never bring those two people back.
Now the sad fact was that firstly, the verge to the nearside was very flat and wide enough to have accommodated the car and caravan, and the ground was very hard, so supportive enough too, but only a few hundred metres further ahead was a rest area where they could possibly have limped to and done the change in complete safety. The signs for that were clearly visible in the photographs that we took.
The point is, that no matter how safe someone might think they are, you can never account for the reactions (or not) of other motorists. Personally, I'd rather completely ruin a tyre (and a wheel if necessary) to get to safety.