The FBI didn't need a warrant to search the home of the Almasri family in Florida, who departed "suspiciously" for Saudi Arabia shortly after 9/11. All they needed was to tag along with representatives of the homeowners association, who had the right to enter houses falling under the association agreement for "maintenance, alteration, or repair." Besides that, the Almasris were late paying their association dues.
This Miami Herald story has the details, including this contextual tidbit: Such a tool, while apparently never used in the context of a terrorist investigation, is frequently used by police who have suspicions but not enough evidence for a search warrant, said Milton Hirsch, a Miami defense lawyer and author of a legal text on criminal procedure.
"It happens every day," Hirsch said. "There is a substantial body of law that allows law enforcement to accompany others who have authority to enter private property—motel operators, college roommates."
That's a loophole big enough for an entire constitutional amendment to get lost in.