"I don't know what video's you've watched but I think you're confused. Fuel gas first is the same order of doing things. You turn the fuel gas on first so you have something to light and you turn the fuel gas off first to extinguish the flame."
Apparently there are two schools of thought on this. I just re-watched the Victor Oxy-Fuel safety video that they have on their website and it clearly shows fuel gas on first when lighting and Oxygen off first when extinguishing.
http://victortechnologies.com/Shop_Talk/Victor/shoptalk.php at 29:53