I have to admit 111 have always erred on the side of caution and probably gone too far when not needed, ie sending ambulances out for my DS when I really just wanted an OOH appointment. I've always found them really helpful and have always rang back in the allocated window.
However, I would probably be one of those parents whereby if I didn't get a phone call back, I'd be ringing or taking to A&E to cover all bases. I think some kind of autonomy needs to be given back to the callers in this situation, so rather than being reliant on a phone call in x number of hours, they are told 'if you have any concerns or we haven't called you back, go to a&e'.
Thing is we are a nation of two sides - those who don't like to trouble the health services and think they are overreacting and don't trust their own judgement and those who use emergency services like taxis and drop in centres when conditions are perfectly treatable at home. You only have to look at some of the topics on here where people are pondering whether to go to A&E or walk in centre to know we all doubt our own judgement and I think that is exemplified when a nurse or HCA tells a parent or patient on the phone to wait.