"The case began when LAPD officers responded to reports of a street robbery near Venice Boulevard and Magnolia Avenue. They pursued a suspect to an apartment building, heard shouting inside a unit and knocked on the door."
This sounds like they had a pretty good reason to search, not like they were just fishing around.
They probably could have pulled a warrant, but the law does allow them to ask permission and enter if granted.
This is the exact same right that says, if I come to visit you (as a friend) and knock on your door, you can give me permission to come in, or tell me to go away.
Police are also people, and you can give them permission to come in, or tell them to go away.
In the latter case, they can elect to pull a warrant with a judge, if they have probable cause, as already defined by law. The judge serves as an oversight to make sure they are not 'fishing.'