Rick Murchison once bubbled...
... Uncle Ricky climbs onto soapbox...
I don't know where this dangerous and misleading hair splitting statement got its origin, or why it keeps its life, but the facts are:
Practically nothing is "flammable" by itself. The ingredients for a classic fire are enough heat for ignition, fuel and oxygen. Whether you call the fuel flammable and the oxygen the accelerator or the other way around is irrelevant. Pure oxygen will cause fire where no fire would be without it, as will adding fuel to a pure oxygen environment. You get the same BOOM regardless of your definition.
If you intend to handle rich mixes, and especially if you plan to mix them yourself, please get (at a minimum) a copy of Vance Harlow's Oxygen Hacker's Companion and read it cover-to-cover before proceding.
Better yet, if you can get your hands on the old Navy training film "The Man From LOX" do so and watch it.
If I sound a bit harsh in my criticism of the common knowledge that "O2 is not flammable" it is intentional. Oxygen is not to be trifled with - it is dangerous in the exterme - it can cause fires you can't extinguish, or deadly explosions. It can be used safely, and should be used by any serious technical diver. But you absolutely must know what you're dealing with or sooner or later it will bite you.
Rick