It might have seemed that Adam's reputation was unreasonably low. After all, he was just a simple guy until recently, and as a Phantom, he had existed for about 50 days.
Was it possible to do so much wrong in that time to get an F-Rank?
Many people would think that there are better candidates for F-Rank. What about murderers? What about rude and immoral people whose actions are not ready to be accepted by the majority of society? What about criminals?
Well... The situation was such that Adam already fell under each of these criteria. Did he kill a person? - Yes, and it happened in front of dozens of people. Did he engage in immoral behavior? - yes, he didn't care about the feelings of the woman, the mother of the dead Phantom.
But... was Adam a criminal? Sure! Only criminals would be out of jail after murder, wouldn't they?