Imagine if it were you. You're at work; you get arrested for killing a couple of guys. The police are asking you questions. Suddenly, from out of the blue, someone asks:
"By the way, did you make a trip to Vegas earlier this year?"
You haven't even been thinking about your trip to Vegas. And at no time, did it ever cross your mind to lie about it. And now, you don't even have time to think about whether to lie about it. You can't even deliberate about it. But, you know that the very fact that they asked you about it means that they know that you went. So, what are you going to say?
"Yeah, I went out there. I did a little gambling; took in a few shows. What of it?"
You're not going to lie about it. For one: you have no reason to lie about it. It's not as though you held up the Palazzo. But for two, if they asked you about it, it means that they know that you went, and it would be futile to lie about it.
And why would Oswald have any inclination to lie? Because he sought a visa to Russia and Cuba? But, he already told them that he went to Russia. And he already told them about the FPFC. In New Orleans, he went on the radio advocating for Castro. He didn't keep his sympathies a secret. He wore it like a badge of honor. And if he actually had gotten a visa and gone, that wouldn't have been a secret either.
Oswald's alleged trip to Mexico City was totally unrelated to what was happening on 11/22/63. Oswald could not have been plotting to kill Kennedy at that time. You can't plot to kill someone unless you have an opportunity to do it. Oswald's opportunity didn't arise, theoretically, until November 20, or so when he found out about the motorcade route (again, it's theoretical). Prior to that, killing Kennedy was a complete void, a complete non-thought, a complete zero. Therefore, going to Mexico was irrelevant. Why would he lie about something irrelevant? But, most important, the very act of asking him about it meant that they knew about it, and therefore, what would be the point of lying about it?
Oswald was being charged with double murder. So, why would he bold-faced lie to police about an innocent, irrelevant thing? If he would lie to them about something as innocuous as that, wouldn't he lie to them about the murders he committed? Wouldn't he think that way that it would look that way? Wouldn't he realize that lying would destroy his credibility? So, why would he lie about a nothing-thing when his very life was on the line?
Again, if it were you, and you knew you were innocent, wouldn't you be scrupulously honest about all things, large and small?
Oswald denied going to Mexico City. He even put it in context, that he had been to Tijuana but not to Mexico City. I would say that that was clever except that I doubt that it was. He was just being honest. He was just being spontaneous. He was just being sincere. But unwittingly, he beat them at their own game because that has the ring of truth.
Oswald did NOT go to Mexico City, and all the evidence for it is contrived, including the lip-flapping, the photos of impostors, the voice recording of an impostor- and really, it's disgusting. If he really went there, they would have photographs of him there, the real him, in Mexico City doing the stuff they said he did. They would have photographs of him galore.