Very good question, the answer is....
Tell it to the judge, and let him/her answer it by issuing, or not, a search warrant.
Well I respect your opinion, though I suspect if you actually were faced with a situation where every second was critical, that opinion might change. The case in the article of course does not rise to that level, and therefore they should have sought the warrant. In fact they should have known what the outcome would be, or at least have reasonably been aware that the outcome was a real possibility.