I don't know that anyone claimed that a bug similar or analogous to heartbleed couldn't be reproduced in Rust. If they did, that was certainly an overstatement. I think more concretely people claimed that unreachable code yields a warning in Rust, which is absolutely true, but certainly not equivalent to saying something like a heartbleed bug would not happen.

In general, Rust is fairly aggressive about linting for "small" details like unused variables, unreachable code, names that don't conform to expected conventions, unnecessary `mut` annotations, and so forth. I've found that these lints are surprisingly effective at catching bugs.

In particular, the lints about unused variables and unreachable code regularly catch bugs for me. These are invariably simple oversights ("just plain forgot to write the code I meant to write which would have used that variable"), but they would have caused devious problems that would have been quite a pain to track down.

I've also found that detailed use of types is similarly a great way to ensure that bugs like heartbleed are less common. Basically making sure that your types match as precisely as possible the shape of your data -- with no extra cases or weird hacks -- will help steer your code in the right direction. This is a technique you can apply in any language, but good, lightweight support for algebraic data types really makes it easier to do.