Tons of people subject to police intervention lie, obfuscate, attempt to exercise power of a sort, etc. It is LE's job to evaluate the situation. Their hands are not tied to making a superficial assessment or taking people's words for it.
.....and I believe LE did the best evaluation of the situation they could do with the information they had
For whatever reason, the consensus decision was taken to treat BL as a DV victim and GL as the abuser.
.........and the Reason from the evidence was BL was a Victim and Gabby was the abuser. Hindsight is 20/20.
And when something big goes wrong or missed, there absolutely is or should be an investigation and review of every step of the actions taken.