I should also mention, (going from previous experience being in hospital) sometimes if the reading is a bit low, get them to take a few deep breaths and see if that changes the reading, particularly if they've been asleep or very inactive for awhile (I.e. Watching a movie intently or snoozing etc) that can often "fix" the low sats.
Asthma is pretty well the most overdiagnosed disease. doctors have thought I had asthma my entire life, and through my own diagnoses and a good doctor, we figured out my entire life I've had allergies which caused seasonal breathing problems. It only took about 22 years to figure it out (I'm 23 now lol) id suggest to the doc to perhaps look into it further, do they have sinus problems? Any allergies? They don't always manifest as sneezing and watery eyes, my nephew gets an itchy roof of the mouth when he has allergies. And even the post nasal drip cough (often the night time cough) so it might be worth looking deeper into?