Of course, the officer can be asked their side of the story, which will be accepted as an eyewitness (single indirection).
So anything you say can (and will) be used against you y the prosecution, but almost never in your own defense. Many people understand at least the basic concept that your words can be used against you, but the fact that those same words cannot help you in most cases is not addressed very often.
(this topic is discussed in the famous - and VERY HIGHLY recommended viewing - video that hoaTeRo linked to, "Dont(sic) Talk to Police" ( https://www.youtube.com/watch?v=6wXkI4t7nuc ) )
Edit: this is literally what happens in Ken's hypothetical story. If the subject didn't lie about the phone call, they couldn't be charged with a false statement.
No. LAWYER UP AND SHUT UP.
If the prosecutor wants to push it, almost any interaction with the police can be made to seem incriminating.
"If you give me six lines written by the hand of the most honest of men, I will find something in them which will hang him." – Cardinal Richelieu, 1641
It seems law enforcement never really changes.
The police version of "lie" is to state something that actually is untrue.
The difference is important because human memory is fallible. You can "lie to the police" while saying nothing but what you believe to be the truth.
"It's OK to talk to the police as long as you don't lie" may be true, but it's also completely useless, because it's impossible to guarantee.