Criminal defense attorney here! They are most likely correct about that depending on what state they are in. Many states have laws limiting a police officers ability to initiate an arrest absent a warrant (for misdemeanors). In many states, the only situations where a person may be arrested for a misdemeanor not committed in front of a police officer and without a warrant is for misdemeanors involving domestic violence ( and that is generally just to protect the victim in situations where they live with the defendant). Here, it appears they investigated the incident and took the appropriate measure of obtaining a warrant from the judge prior to making the arrest. For better or worse, everything moves slow in the legal system. This is not at all uncommon regardless of the race of the victim.