If a patient in hospital is continuously on 02, would it be true to say that the person is hypoxic irrespective of the reason the person needs the 02?

Probably : However in some cases oxygen is given when the patient is not hypoxia eg critical illness or child with breathing problems or palliative care

NO: No, this would not be true to say. There are many reasons a patient without hypoxia might benefit from oxygen therapy. This article lists 9 indications for oxygen therapy and only 3 of them involve hypoxia: http://www.gosh.nhs.uk/health-professionals/clinical-guidelines/oxygen-therapy-administration-non-emergency-situation

No!: O-2 in hospital is often given to patients who have NORMAL O-2 Saturation but who are AT RISK for hypoxia! Hope this helps! Dr Z