The Supreme Court has repeatedly ruled that they cannot arrest you in your home without a warrant unless there are exigent circumstances. They could have witnessed you actually do the crime but they would still need a warrant.
It does not appear the police “broke” into the house in this case.
If you open the door to police, they can consider that an invitation to enter the house.
With all the cameras now in society, police are being held to higher standards than they were formerly.
It only takes one officer at the scene to push through an opened door. The others will feel an obligation to back that officer up.
In this case the department will pay for the officers mistake.
That is a horrible thing. Opening the door, by itself, is not under any circumstances an invitation to enter. Invitation to enter is entirely separate from opening the door.
the department will pay for the officers mistake.
There's your problem.
"Mistake" == "Violation of the law"
The department didn't violate the law.
The local government didn't violate the law.
The TAXPAYERS didn't violate the law.
The individual PUBLIC SERVANTS violated the law. The individual PUBLIC SERVANTS need to pay for their violations of the law, individually and personally, in both civil and criminal court.