Go back and read the story.
Hot pursuit is when you are chasing the guy with him in sight.
Hot pursuit is when you see him go in the house.
In the story you are talking about, there was no pursuit. The cops wanted to set up an observation point, spying position, whatever you want to call it but it was not in pursuit of a guy that had just committed a crime.
In the case by the OP, it was hot pursuit. Yes, in my other “observation” story, it was not hot pursuit. Hot pursuit has nothing to do with “going into a house”, but onto or into property. In the case by OP, the criminal was pursued into the backyard. The LEO was pursuing the perp and saw the perp go into the backyard, and hide. Yes, according to law, the LEO had the right to enter the backyard to pursue the perp. The protection of the public outweighs the privacy rights of property owners, with a few exceptions. But darnit, stop the stupid arbitrary shooting of dogs. One can tell within a few seconds whether the dog will be hostile or not. If the LEO cannot determine this, put him on desk duty. That’s BS.
My story involved LEO who did not care if the owner protested or not—they took over the private property. The similarity is the LEO entered onto private property in both cases without any consideration for the property owner.