True, at some point intuitions come into play (unless you are some kind of Spock), to determine your personal moral bedrock. But at least for me, these intuitions are not all born equal, and not all intuitions are part of this bedrock.

A typical example would be: 'Cute animals are more important', which may conflict with some deeper rule in some situation. Instead of just following my intuition with that first rule, I think my moral judgements are better when I take a step back and try to use the deeper rule.