The fourth Amendment died when "probable cause" searches were invented. The constitution says the order is: (1) probable cause; (2) oath or affirmation; (3) warrant; (4) search or seizure. Today the order supposedly is: (1) probable cause; (2) search or seizure; (3) oath or affirmation, in an affidavit of PC; (4) "warrant," meaning a retroactive judicial blessing.
If you accept searches on probable cause, and if you believe their report that the arrestee had partly entered the living room, then they were within bounds: they glanced around the living room looking for accomplices or other dangers, and they noticed the butt of a pistol sticking out in plain view. We all know the report is a lie, of course. He was probably arrested outside on the lawn, and there wasn't any gun in plain view--they tossed the place. But if you believe their perjured testimony, then they were correctly executing a "cursory safety check" that was "incident to the arrest."
Now it does bother me that they're most likely lying. But the real problem is the entire concept of "probable cause." If you really have probable cause, then go get a warrant. Maybe it does "make the cops' job harder," but that's just too bad. The rights of the innocent are paramount. (OK, even that's too authoritarian for me. I don't actually believe anyone should have the power to issue a "warrant" to invade my private property. But I'm just talking about the Constitution here.)