Safety Concerns

Recently on my general surgery patient i had a bit of a dilemma with monitoring a pt in a treatment session. One of my patient's had quite low sats at rest and the medical team had advised me to maintain these at 90-93%. This patient had worked in a oil refinery for 30 years and had regular secretions as well as a past medical history of Parkinson's. I found i recent times when i walked this pagtient and advised him to concentrate on taking deep breaths his sats would improve and maintain 93-94% so i was reluctant to increase his oxygen therapy as the objective was to decrease it to get him discharged. This one particular occasion i noticed that my oxygen cylinder was low and would need replacing after seeing this one patient so i risked using it because i didnt require much oxygen with this patient anyway, on 2l via NP his sats were fine. However this particular time my patient desaturated to 85% but i found it really hard to believe; i know sats monitors can be inaccurate but he had no increased SOB, i had allowed for a rest, and he was having a conversation with me. I wasnt far from his room so i didnt panic and just kept monitoring him making sure subjectively he was not desaturating. Suddenly a physio from the other ward came rushing past me and noticed that this patients sats had dropped. Instead of asking me if this was usual for him she grabbed the oxygen cylinder turned it up to 4l (i had him on 1l with NP) and started rushing around so the patient would get to the chair in his room. The oxygen cylinder had almost run out so it looked really irresponsible on my part. I asked the patient how he felt and he reported that he was feeling fine he felt he did not need the oxygen therapy increased and that the reason why he looked unsteady was because he was trying to take big steps because with his Parkinsons as he starts to adopt the festinating gait pattern. I assessed his sats at rest and they continued to stay at 90% on room air. His sats for the last few days on room air had been at this level . I explained everything to my supervisor after and she felt that if he did not use oxygen therapy at home and we want to send him home, its important to start wheening patient's off oxygen despite the fact that their sats are lower. I know we are taught to be conservative with pt sats, but what are everybody's thoughts on using the oximeter and how accurate it is?