I think a few other lines from other episodes shed light on the way his mind works. Things like, "I never tell the truth because I don't believe there is such a thing," or "The truth is usually just an excuse for a lack of imagination."
I would say Garak's opinion is that truth is subjective - every person has a different view of what the 'truth' is, from their own perspective. And I suppose Garak is just someone who accepts that, and works with it rather than trying to force one objective version of 'truth' into a situation.
Look at the show as a whole - we see it as Sisko being the big hero. But Dukat would think he was the hero and Sisko was the villain, unfairly blocking him from his rightful place as the master of the galaxy. Which one is the truth? It depends.
One of Garak's stories in "The Wire" is about his 'friend' Elim. He explains how he tried to betray his friend Elim and blame everything on him, only to find that Elim had beaten him to it. Then we find out that Elim is
Garak, they are the same person. So what we have to take from that is that Garak believes he betrayed himself - in other words, that everything that happened was his own fault.
From one perspective, the 'Elim' story was a complete lie. From another, it's totally the truth.
So I guess what Garak is trying to teach Bashir in that "Even the lies" scene is that there is truth in every lie. Something there is true as someone understands it. You can't say that something is a complete lie or a complete truth, because someone else would see it differently. That's how Garak's mind works - he accepts that and goes with it - and he probably sees it as vital to surviving in the world to which he was accustomed. And now he's trying to teach that to Bashir, to broaden the doctor's mind from the typically Starfleet black-and-white to a more Cardassian grey.
And yes, I think it does signify the way both characters develop over the course of the show. Garak is teaching Bashir, but Bashir is teaching Garak at the same time. They practically swap places. Bashir becomes suspicious, distrustful, involved in shady dealings and nefarious secret organisations. Garak becomes one of the team, working for the greater good, a trusted friend and confidant, a righter of wrongs.
And it could be said that that begins in "The Wire," with Garak opening Bashir's eyes to the complexities of life and truth. And at the same time, Bashir is showing Garak what it is to be a friend, by staying by his side no matter what the truth may or may not be.