They're allowed to lie to suspects, not the courts where parallel construction happens. A defense attorney can't get evidence stricken when it came from dubious sources when they lie in court about the source.
That's only true in theory. In practice, police lies are one of the pillars of the US "justice" system.
https://en.wikipedia.org/wiki/Police_perjury
https://www.nytimes.com/2018/03/18/nyregion/testilying-polic...
https://slate.com/news-and-politics/2020/08/police-testilyin...
https://web.archive.org/web/20130809014315/https://www.reute...