I agree with you, but it doesn't change the implications of a police officer having a complaint and a sufficient description to follow up on it without a warrant.
It is at their discretion, same as if you called in that your grandma didn't answer the phone, they could ignore it or bust down the door. Both would be fully legal.
Court is a different matter. A judge could say there wasn't cause to search after the fact, but that won't change what the police do in the moment.