Why do we need to fly at lower altitudes at night to prevent hypoxia?
The main reason stated by aviation authorities is due to the impairment of vision, your rods provide the majority of your sight in low light conditions and are affected by the lower oxygen levels. However, your colour perception (provided by your eye's cones) is also affected and this is already degraded at night due to the lower light levels.

The below quote is from an EASA General Aviation Safety Briefing on Preventing Hypoxia


  Hypoxia also impairs night vision. Because the rod cells in the eye, which give us night vision, require a lot of oxygen, a lack of oxygen causes visual impairment.


Regarding your friend's point on the diurnal atmospheric changes, this should not be a factor as the suggested altitudes by the aviation authorities on hypoxia prevention should be given as a pressure altitude (i.e. the altitude with the standard altimeter setting of 29.92 inHg or 1013Hpa)

Hope this helps