There is another reason why thinking Oswald lied about Mexico City doesn't make sense. It is that people generally anticipate and prepare for their lies. They may even rehearse them. But, when a person is put on the spot, where he isn't the least bit prepared, where he hasn't even decided to lie, then he will very likely tell the truth.
Oswald had no reason to lie about Mexico City. Even according to the phony story, he didn't commit any crimes there. And, it wasn't against the law to visit the Russian and Cuban embassies seeking a visa. And he certainly was not one to keep his accolades for living under Communism a secret. He was proud of it, wasn't he?
Now, when he was arrested on 11/22/63, he certainly wasn't thinking about Mexico City- even if he had gone there. And while he was waiting to be interviewed, he may have wondered what they were going to ask him, but he certainly didn't expect them to ask him about Mexico City. So, that question must have caught him by surprise, again, even if he went there. There is no reason to think he had made a decision to lie about it- or given it any thought to it at all. So, when the question came, he would have had to deliberate. Before he lied, he would have had to think about it, which would have taken time. And the very pause, the very delay would have given away that he was lying. So, the odds are very great that, being unprepared to lie, he would have told the truth. And the truth was that he didn't go to Mexico City.
And, it's interesting that he added the framing statement that the only place he'd been in Mexico was Tijuana. That's because it was an honest thought; it was just a natural mental progression- one that he had just as anyone could have. It really, truly comes across as HONEST.
Oswald didn't go to Mexico City, and real Oswald defenders should have no trouble accepting it. Those who do have trouble are NOT real Oswald defenders.