Staging of copd is based on airway obstruction as shown by the fev1 test and fev1/fvc ratio - generally described as lung function tests or pulmonary function tests. As above, staging is not based on whether or not you need oxygen. You don't give your results for these test results but moderate as per the GOLD index (Global Obstructive Lung Disease) is between 50-80% of what would be predicted for your age, weight and height. So to me, what your doc is telling you is muddling and unhelpful.
Just to give you a personal example, I am at the severe stage, well into it at 36% fev1. I have been on ambulatory oxygen following exacerbations and hospitalisation (when I was on it 24/7) but due to the amount of exercise I do, I have managed to improve my muscle tone enough to not need the oxygen when I am well. Exercise is very important as copd often makes the muscles decondition, but muscles which are kept in good nick will make more efficient use of whatever O2 you still have. People vary wildly across the various stages of copd in what their oxygen needs are.
You clearly need more information. I think it is too easy to say not to worry because you will - I certainly did. I think its inflammatory and frankly stupid for your doc to use a phrase like "hanging by a thread". Are you in the UK? If so, and even if you aren't, please consider calling the BLF helpline on 03000 030 555, armed with your test results (ask for them to be sent to you if you don't have them) and talk through your situation. The nurses on the helpline are friendly and high knowledgeable. And you will get the benefit of their knowledge which may well make you feel more in control.