I don't think this article is making a claim about whether or not these phrases indicate that someone is about to lie to you.
The phrases themselves are often untrue.
For example, if I say "It’s not about the money, but...", what follows is not necessarily a lie. What the article claims is that I'm about to make an argument based on money and that I'm trying to preemptively deflect any counter-argument. Therefore, the phrase "It’s not about the money, but..." may, strictly speaking, become untrue. But that doesn't necessarily have any bearing on what follows.
The phrases themselves are often untrue.
For example, if I say "It’s not about the money, but...", what follows is not necessarily a lie. What the article claims is that I'm about to make an argument based on money and that I'm trying to preemptively deflect any counter-argument. Therefore, the phrase "It’s not about the money, but..." may, strictly speaking, become untrue. But that doesn't necessarily have any bearing on what follows.