You should take a first responder course, as was mentioned, but oxygen really is the safest "drug" that we carry on our units, and there are very few conditions that it may worsen. (underwater is obviously another story). In the field, we won't withold it from anyone who needs it . There are currently no field contraindications to supplemental oxygen in the state of California, and I doubt there are in other states either (keep in mind that "field contraindications" means short term administration, such as the 20 minutes you described). If you have the one tank (even two) of oxygen in a DAN kit, you will not be able to administer oxygen long enough to reach toxic levels on land. But even as a paramedic, I am not allowed to practice as one off duty and oxygen falls under the drug protocols.
I would be careful about administering oxygen outside of your "protocol" (in other words, what your DAN certification allows), but this where the dilemma lies. Sometimes the life safety issue may outweigh the potential trouble someone may cause you later for it. If my dad was at my house and started having chest pains, you bet I would get my O2 kit and give him oxygen until EMS arrived, and honestly I probably would have done the same in your situation. I realize that when you are dealing with strangers, concerns about someone coming back with legal issues later on are greater, so you have to make your own decision.
With a dive injury, it's obvious, give the oxygen as needed.