He kinda contradicts himself. "Then took the other, as just as fair, / And having perhaps the better claim, / Because it was grassy and wanted wear;" seems to imply that the one he took was indeed "less traveled"; but then, immediately, "Though as for that the passing there / Had worn them really about the same,". It doesn't seem to me that there's any Right Answer to the question: Are we supposed to understand that the path he took really was less-travelled, or not?
My reading of the last stanza differs from yours: he's not saying that he'll tell people, falsely, that it set the course of his life; he's saying that although he couldn't see any good reason for choosing one over the other, as his life goes on it'll turn out that it made a big difference.
The thing that intrigues me about this poem (which, actually, I don't much care for despite its fame) is the title. "The road not taken". That's not the perhaps-less-worn path he did take, it's the other one. Without that title, if you asked me which path was more the subject of the poem I'd have said without hesitation: the one he took, which "has made all the difference". But no: the spotlight is on that sigh with which Frost will be telling the story, the regret (if that's the right word) that he couldn't try them both. I think.