Almost but not quite. You are promised that safe Rust doesn't have Undefined Behaviour, but that's cultural, not technological. The technology is just enabling Rust's culture to deliver what they promised, but it would be very easy to purposefully (indeed there are known bugs where it does happen, look for "Rust soundness bug" if you want examples) inject UB which happens in your safe Rust.

The extent to which this is about culture should not be underestimated, to me that's the most hilarious part of Bjarne Stroustrup's big rant on memory safety a few years ago. The C word appears exactly once in his slides, in a quote from somebody else about what needs fixing. But Bjarne never addresses this once, even though it's the actual problem.