It's a weird one, you can enter if you reasonably believe there's cause to need to render emergency aid. But here's my understanding of the sticking point as an absolutely not legal-professional.

I think any evidence gathered in those circumstances would not normally be admissible in any kind of criminal proceedings unless they also met the normal probable cause standards for entry. Like it's not automatically trespassing for them to be there for emergency aid, but gathering unrelated criminal evidence at the same time would be basically a warrantless search.

But because a crime was committed as the officers were there to render emergency aid, the court allowed evidence gathered in the home relating to the "assaulting an officer" charge to stay on the record. It seems kind of reasonable on the surface, but it does open up a whole can of worms whereby a corrupt police could maybe legally get away with entering your home because they heard a scream, hoping you're belligerent enough with them to commit some form of crime they can then charge you with.