You're incorrect in your belief that unintentionally providing incorrect information to police, in a criminal matter(one can legally lie to the police all day, if it isn't in the course of their "official duties" and one isn't being questioned in the course of an investigation or other "official matter". Outside of "official duties", law enforcement officials are just regular members of society. The caveat to that is if your lie causes law enforcement to bring charges against a person that didn't commit the alleged criminal act, that lie is also a crime.), is a crime. Providing false information to law enforcement requires "intent", yet you falsely claim that "making a mistake"(whereas a "mistake" implies one did wrong unintentionally) is sufficient is endure the punishment of a felonious act. You couldn't be more wrong.
As an ex-law enforcement officer myself, I can tell you that Bennett Haselton is an idiot(and completely wrong, too), and you, MisterSquid, while most likely well intentioned(I hope so, at least), are also wrong. I should also point out that intentionally providing false information to law enforcement, in all circumstances, isn't a felony, in all jurisdictions. Case in point, in Georgia, according to O.C.G.A. 16-10-25, providing false identifying information to law enforcement is a misdemeanor, and it also requires "intent".
I will hold one caveat to my view of your information, in that the "super cool" all caps "DO NOT TALK TO THE POLICE WITHOUT THE PRESENCE OF YOUR ATTORNEY" comment is correct, though, with a slight alteration, or two. It is: Do not talk to the police.
Most, if not all, defense attorneys will forcefully suggest that course of action. The only time that might not be true is when there is strong evidence that the targeted suspect is innocent, or at least not guilty of the criminal act(s) in question, and that another person is. One can never "talk" his or her way out of suspicion, but substantial evidence can help move the focused suspicion onto someone else.
I do believe that one area of lying is left out(which I commented on earlier in this post), and it is equally important. If one lie to law enforcement, and that lie causes the arrest and conviction(thought conviction is necessary to bring charges for the lie(s)) of a person that isn't guilty of the crimes at issue, the liar(or liars) has committed a criminal act. If it is to the police, usually the crime is the filing of a false report to the police. If one lies on the stand, in court, it would be perjury, both of which also require "intent".
All of this hinges upon "intent", which a "mistake" doesn't hold.