Heartbleed implemented their own memory management system (and had a bug in their use of it). This is pretty unusual even in C. It's extremely unusual in Rust, but who's to say that a similar implementation in Rust would come across the same challenges and implement their own memory management too? And write the same bug? Ultimately this kind of system would be unsafe code anyway, so Rust won't help you there. The question is if a Rust programmer would design such a thing (it's very non-Rust-y). The answer is probably "no". However, the same can be said about C programmers and the heartbleed code, so you have a bit of a no-true-scotsman vibe happening here.

So, yes, heartbleed could have happened in Rust too. I do feel it's less likely (Rust more strongly forces you to compartmentalize unsafe abstractions), but all of that is really debatable.