You need evidence of a crime to get a warrant, don't you?
Otherwise, can't someone harass anyone they wanted to with accusations?????
In fact, doesn't this happen all day long?
The warrant comes when it's likely that someone has/is engaging in criminal activity, but they can't just make stuff up in order to gain access. The 4th & 6th Amendments cover this, if the people playing along (Police, prosecutors and judges) are actually following the Constitution.
Last I heard was comments from the Nashville Police chief, saying that she had called to report that she was considering suicide- when they arrived, she was sitting on the porch near two handguns that weren't loaded. She wasn't close enough to them to be a threat, so they cleared the guns from the porch and in talking to her, they decided that she needed some mental health care. He wasn't there and she didn't seem like a reliable source to make a probable cause argument.
If a drug or bomb detecting dog had been going nuts outside of the fence as soon as they got there, it's possible that a warrant might have been granted.