Science rests on an 'a priori' assumption of naturalism and is deliberately limited as a worldview. As such, it is an inferior position for judging reality as it considers only one possibility (that of naturalism).
It is unfortunate to see parents so uninformed about what science is and what it isn't that they automatically assume the 'scientific' perspective is superior when it is in fact, the inferior position.
This lack of critical-thinking skills is one of the unavoidable consequences of limiting acceptable worldviews to 'naturalist only'.
You are right, science is limited to that which can be observed.
On the other hand, we have magic, superstition, wishful thinking, divine revelation, what the stars foretell and what the neighbors think, public opinion, Ouija boards, tarot cards, witch doctors, the unguessable verdict of history, and a host of other un-natural phenomena.
Thanks, I'll stick with science. It doesn't seem that inferior a method for judging reality when one considers the alternatives.