It's important to understand the truth of Fourth Amendment requirements, and this article is misleading. A warrantless search of the home is a per se violation of the Fourth Amendment. However, warrantless entries that fall under narrow exceptions are not violations. The hot pursuit exception allows police to enter into a home without a warrant while pursuing a felony suspect. The entry is limited in scope to searching for that individual and does not include rifling through drawers, etc. However, illegal activities or items that are in plain view while the officers are searching for the suspect may lead to an arrest.

If challenged, the validity of the hot pursuit search will be reviewed under the totality of the circumstances. First, did the police have reason to believe the suspect fled into the home? Second, if there were illegal activities or items, were they within the scope of the search for the suspect?

There is no requirement that a police officer show you a search warrant. If no warrant exists and entry does not fall under an exception, the search is unconstitutional. But failure to provide the warrant for review does not amount to an invalid entry.

That is not to say you shouldn't ask. In this situation the residents were dealing with plainclothes officers. Seeing a warrant would make a person feel better about opening the door. But it's not required. And if you don't want them to come in, don't consent. They might come in anyway, but they won't have your consent and the validity can be challenged after.

The officer in this video was correct about what he was saying, though that doesn't mean their actions were valid. They could potentially enter without a warrant. That doesn't mean they actually had reason to believe the suspect was there (he sounded a bit shady when explaining their search).

There is not enough information here to know whether their entry was constitutional. We rightfully tend to disdain anything that appears as abuse. But it honestly isn't fair to do so from the little any of us can know here.

I'm not suggesting any of these things (exceptions to the warrant requirement, no requirement to show warrant, etc.) are good or bad ideas. I'm only saying it is currently the law and has been for a while.