It depends. There can be false pulse oximeter readings sure, in cases of hypoperfusion (e.g Raynaud's disease), nail varnish or incorrect use but finger tip sats probe are fairly easy to use, if somebody called me with COVID symptoms with repeated Sats readings in the 80s yeah I'd be confident they should be phoning 111 or an ambulance if symptoms suggestive of respiratory distress
There are some instances for example where we accept low Sats readings, e.g. COPD patients or a recovering infant with bronchiolitis. But its an important clinical vital sign, and in the case of COVID (after respiratory rate) probably the most important factor in deciding whether somebody needs an admission or not. There are plenty of clinical symptoms though however people need to be mindful of, severe shortness of breath and fatigue are red flags.
I'd recommend the paediatric ones still, there's one for kids aged around 2-12 years old, neonatal ones for younger than that. Accuracy for adult ones on kids is less, I think its to do with finger diameter and the sensors