There are plenty of exceptions to the hearsay rule, though; there are also times when something that seems like it’s hearsay isn’t. Exception: maybe you made the statement to the cop while you were covered in blood and blubbering about something you had witnessed, making it an excited utterance. Or maybe your lawyer is eliciting the statement from the cop not to suggest to the jury that it’s true, but to show you had no motive, making it fall outside of the hearsay rule.

Police have a responsibility to testify truthfully under oath, within the constraints of the rules on hearsay. But that doesn’t mean they are forbidden from saying anything in your favor, no matter what.