I'm not sure that exigent circumstances would stand up if court if this had gone there. From the Wikipedia you linked:
However the officer himself said, '“So why don’t we just write a search warrant,” the officer wearing the body camera says to Payne.Exigent circumstances may make a warrantless search constitutional if probable cause exists.
“They don’t have PC,” Payne responds, using the abbreviation for probable cause, which police must have to get a warrant for search and seizure.'
So on the record stating that no probable cause existed at that time.
I absolutely agree that the people involved dealt with this situation very well afterwards.