The sad truth, my friend, is that the cops can legally tell you anything they want to get an arrest, and they do. I have first-hand experience with such. The detective who “interviewed” me tried several times to bait me into an admission of crimes that never happened, insinuating that my victim made those claims… even though I was honest and forthcoming nearly from the beginning about what I had done. My step-brother is a detective in another town, and he has confirmed that they are allowed to make false statements to suspects in order to secure a confession. My step-mom almost disowned him for that one.