Memory safety vulnerabilities basically boil down to following causes: null pointer dereferences, use-after-free (/dangling stack pointers), uninitialized memory, array out-of-bounds, and type confusion. Now, strictly speaking, in a memory-safe languages, you're guaranteed not to get uncontrollable behavior in any of these cases, but if the result is a thrown exception or panic or similar, your program is still crashing. And I think for your purposes, such a crash isn't meaningfully better than C's well-things-are-going-haywire.

That said, use-after-free and uninitialized memory vulnerabilities are completely impossible in a GC language--you're not going to even get a controlled crash. In a language like Rust or even C++ in some cases, these issues are effectively mitigated to the point where I'm able to trust that it's not the cause of anything I'm seeing. Null-pointer dereferences are not effectively mitigated against in Java, but in Rust (which has nullability as part of the type), it does end up being effectively mitigated. This does leave out-of-bounds and type confusion as two errors that are not effectively mitigated by even safe languages, although they might end up being safer in practice.