The "you might even say 2006" links to Graydon (aka 'that dude')'s initial commits. There's no discrepancy here. The Rust Project, aka the whole apparatus around developing Rust, started at Mozilla in 2010. The language was a personal project for just Graydon before that. They're two related but distinct things, and you could argue "Rust" started at either of them, depending on in what sense you mean.

That Graydon started Rust on his own in 2006 is not disputed by anyone with knowledge of the facts, including the very post you linked.

You also in your original comment said Mozilla picked it before 2006, which is also impossible and simply incorrect.