Disclosure: I am a former firefighter, a LONG time ago. I also have a minor in chemistry from a loooooong time ago.
Those signs are posted because normal combustibles in the presence of an enhanced oxygen atmosphere can burn curiously and rapidly. For instance a lit cigarette will burn so rapidly it appear to explode. A struck match goes off like a small fire cracker. Cotton sheets and polyester shirts burn like they are soaked in kerosene.
But it’s the combustibles burning NOT the oxygen.
Oxygen is a reagent in the chemical process of “burning.” Oxygen itself CANNOT BURN.