It's not that she doesn't know, she thinks he is a knight o retainer of some sorts, not only that, but her image of the prince is totally bias, even for a detective, thta bias may cause some second hand guesses in a investigation until its the investigator realizes it.
Not to say, it's not like she IS a full fledged investigator with years and years of experience so...
it may be for plots sake too
i already gave up on having her be anything more thna a Sue Mary, I'm going to just appreciate her cuteness.