But they can. You are wrong.
Can we please wait for some more facts to come out before rushing to conclusions?
I'm just kidding, of course we can't.
I think I'm right. Maybe you're a lawyer or something and you can correct me if I'm wrong.
But, surely, you cannot just enter someone's house based on a police officer's subjective belief that there is probable cause. If that was true, there would be no need to get a warrant to search.
There are certain exceptions to the warrant requirement, open view, exigent circumstances, consent to a search, etc. But, there's no just freestanding right to search a person's house because the officer thought there was probably cause.
In this case, it's 100% possible that one of the warrant exceptions applied. But, the assertion that warrants are unnecessary ever, that's ridiculous.
I could be wrong and maybe it's because I am thinking about the dynamic with regard to automobile entry, but a police officer likely can enter a home if there is probable cause (a smell, a sound, etc). The issue is of course if the officer entered without tangible probable cause (as in, made up a totally subjective justification for doing so), then any evidence can be thrown out. Of course, in this case, someone was murdered...