I am not a lawyer, but I know lying to the police is a crime in many of our states and in Federal law. Even telling the truth and misremebering things is considered a lie to the police, but our police can lie about anything and everything. In the states you should NEVER EVER lie to the police since that is a potentially punishable crime and will make it likely that you will be considered guilty of "something" by the police and the Prosecutor . That is why the advice is to answer no questions about a case until you talk to a lawyer is very sound.
And the out of context example of "he never liked the guy" is a valid example. I have seen it where the police were under pressure to find someone, anyone, to arrest for a crime, particularly a murder, then make up....er....find evidence against him, and then have the Prosecutor ramrod it through a trial since that DA is under the pressure to convict someone, anyone, of the crime. If anyone had witnessed the trial of the West Memphis 3 back in '93-'94, you know what I am talking about. The justice system, in some places in the states, is very broken indeed.