The Public Eye police the streets of New York, but are far from law enforcement, they are crooked, armored officers.
The Public Eye act both as a militia for Alchemax, on Earth but also on the Mars mining colonies, and as a remunerated police-force for the public, without caring about the grief. In this optic, rich people such as black-carders weren't targeted or arrested.
One of their mission is to take down the Punisher, because of his free actions, the opposite of the Public Eye's policy: Police's services are non-free, and attacking black-carders criminals. They charge Jake Gallows to take down this vigilante, unknowing he's the Punisher.
They were commissioned by Alchemax to take down the former CEO of ECO Corp, Paul-Philip Ravage.
When Doom successfully take-over USA, he disbands all police force to gather them into one: the SHIELD, and intended to put the Punisher at his head.