No, the "if it compiles, it works" is genuinely about the program being correct rather than just free of memory errors, but it's more of a hyperbolic statement than a statement of fact.
It's a common thing I've experienced and seen a lot of others say that the stricter the language is in what it accepts the more likely it is to be correct by the time you get it to run. It's not just a Rust thing (although I think Rust is _stricter_ and therefore this does hold true more of the time), it's something I've also experienced with C++ and Haskell.
So no, it's not a guarantee, but that quote was never about Rust's guarantees.
I have definitely noticed this when I've tried doing Advent of Code in Rust - by the time my code compiles it typically send out the right answer. It doesn't help me once I don't know whatever algorithm I need to reach for in order to solve it before the heat death of the universe, but it is a somewhat magical feeling when it lasts.
It's a common thing I've experienced and seen a lot of others say that the stricter the language is in what it accepts the more likely it is to be correct by the time you get it to run. It's not just a Rust thing (although I think Rust is _stricter_ and therefore this does hold true more of the time), it's something I've also experienced with C++ and Haskell.
So no, it's not a guarantee, but that quote was never about Rust's guarantees.