Any normal person would not listen to the ramblings of some psychopath,and the first instinct would be to call the police. Patsy asked JR what they should do, because the note said not to call the police. He told her to call the police. As he said in their book, he thought they would put up roadblocks, etc. to try to find her.
Patsy read only the beginning where it said they had their daughter...and she ran upstairs and saw JBR missing and called for John. Their actions seem normal to me. They had no idea that the police would screw things up. I doubt the perp was watching the house, but if he were, he would have seen the police come right up to the house.
Had the Ramseys not done what most people would do, and not call the police, I can only imagine what would have been said about those actions.