Actually, it's a fire "tetrahedron" and that fourth component is "chemical reaction."matt_unique:...02 is part of the fire triangle for sure...

The issue of inexperience on the part of the OP aside, I can tell you that handling O2 fills on a regular basis is not nearly as dangerous as some would think.
I say this because I worked for a fire department that did thousands of high pressure (>2000 PSI) O2 fills per year using more than 500 cylinders and 200 demand regulators of all configurations. We had 2 O2 filling stations with 2200 PSI banks, whips, pigs, etc. Minimal training on filling procedures, minimal cleaning and maintenance on regulators and valves (when it breaks, "fix it") and general apathy in terms of "respecting" O2. We did this for more than 20+ years with no accidents and no fires. I'll bet the thousands of fire and EMS departments in the USA have similar experience and probably near identical results. If a department DID have a TRUE oxygen driven fire with HP cylinder failure and a large release of gas, I'm sure the results would be dramatic enough to make some news.
That said, "HEAT" and "FUEL" are probably the components that drive most O2 related fires at filling stations. The simple way to avoid it is to keep relatively clean equipment, make O2 the FIRST gas to mix and NEVER "jack" (i.e., "pump") O2 for fills. Do the blends on the low side, use air on the high side and keep in mind the cut offs and direction of your gas. It's NOT rocket science.
Just my thoughts...