Hahaha....you are confusing FBI agents with police officers.
Npt even close to the same thing....you cannot get arrested for lying to a police officer.
While you cannot be arrested for
lying, if in court you say you did something and a cop says you said you had done another one that day , even a tiny it of difference in wording from a statement what not, and you will appear the liar in court.
There is always reasonable doubt, but that goes out the window quickly if you are successfully framed as a liar. Even when you do not lie and it is a typo on a date on a paper written by a lawyer’s secretary, they will team up with the DA to nail you for it.