...Thomas Goldstein, the lawyer for Scott Randolph, said it would have taken police only five minutes to get a judge's approval over the telephone for a search warrant...
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I would say that they did.
"The right of the people to be secure in their persons, houses, papers, and effects, against unreasonable searches and seizures, shall not be violated"
"and no warrants shall issue, but upon probable cause, supported by oath or affirmation, and particularly describing the place to be searched, and the persons or things to be seized."
Please note that these are two separate clauses, the first protecting against unreasonable searches, and the second imposing strict conditions before a warrant may be issued. The 4th Amendment does not require that warrants be issued before a search may be undertaken. The Founders hated warrants, since they would allow the police to escape liability in a civil suit, so they added the Warrant Clause to make it difficult for the police to obtain warrants.