I can buy a Kei car in LA and can't drive it.
I can raise fighting roosters and sell them but I can't fight them. I can buy an ambulance, firetruck or police car but cannot operate them. I know a guy who will file down the firing sear on an AR-215....but I digress.
Break it down. A good process to follow is there is ever any question about whether you are allowed to do something.
1. At what level of training did I get this skill? (First aid, first responder? No problem. Higher than that? Need medical direction).
2. Am I allowed to practice this skill without medical direction in the form of a doctor's order, a doctor's prescription, standardized procedures, or standing orders?
Oxygen's a sort of borderline issue. If you read the package for all medical appliances associated with oxygen administration, they read "For use by a doctor's order" or some such, including masks, cannulas, BVM's, etc. (Same for cervical collars too, bunkie).
But the third and biggest question is the "dog-caught-the-car" one:
3. "OK, I used the item, now what?". There are logical and professional sequelae to certain actions. For instance: OK, the pt's on O2. Why? How long will it last? What other treatments are necessary? How about transport? This applies to IV's, traction splints, and ESPECIALLY to spinal immobilization measures. Often, even as an EMT, your best bet if higher level EMS or even just more bodies are available, is to follow the cardinal rules: keep 'em quiet, keep 'em still, call for help early, and assist/address your A-B-C's.
If people are going to use you as their "insurance" to go out into the boonies or some such, think hard about it. Maybe they need to not go there until/unless they are actually able. Are you ready to safely pack out a patient, or go get law enforcement while someone stays with the body if someone expires?
As a side issue, there are also safety issues revolving around carrying pressurized oxidizing gas in unmarked cars or at home. Not to argue about it.B)