No, they are not completely unreliable, and that's where your thesis goes completely off course. If our memories were "completely unreliable," then human civilization would not exist as it so obviously does.
There are simply things we're likely to remember clearly and things we're not.
I may not remember a clown in the background while I'm looking at a beautiful woman, but if that beautiful woman suddenly approaches me and asks permission to kiss me, I'm probably going to remember that kiss. If she tells me her name, I'm more likely to remember that, too, given the unusual circumstance and my emotional connections to the event.