If you lie to someone in order to induce them to give you valuable private information, that's fraud, not "information you carelessly broadcast". If a Stingray says "Hi, I'm a cell tower, connect to me!" that's not at all the same as mere passive recording.
(Now, mind you, mere passive recording of cellphones without a warrant is _also_ an illegal search as far as I know -- or would be if there were still unencrypted data to passively record. But that's totally unrelated to what a Stingray does.)
Law enforcement are permitted to lie to get private information, e.g. in an interrogation. They would need to have at least probable cause if not a warrant to conduct that interrogation though.
(Now, mind you, mere passive recording of cellphones without a warrant is _also_ an illegal search as far as I know -- or would be if there were still unencrypted data to passively record. But that's totally unrelated to what a Stingray does.)