Probably because the injured guy was caught in the mangled vehicle, and couldn't be extracted in time to apply it.
I also wonder why someone didnt use someone’s web belt as a tourniquet. I’d also guess that if the injured guy was caught in the mangled vehicle, and couldn’t be extracted in time to apply a belt, the injured guy couldn’t have tightened a tourni that was biult into his own clothes, either. I’m guessing over-simplification and dramatization from the usual clueless Associated Press reporter.
"Rose could not get his comrade a tourniquet"
The story is poorly written since it leaves out the details and thus is too vague.
In a pinch the web belt around his or the patients' waist can be removed and used as a tourniquet. If he didn't have the ability to place the belt around the leg due to the mangled wreckage that's one thing. If he didn't think to use the belt that's another.