It seems fairly obvious that if Language A's design prevents a certain class of bugs possible in Language B's design, A is safer than B. If someone isn't satisfied by this, they probably are biased against Language A. I'd tell the hypothetical person to try writing a buffer overflow vulnerability in safe Rust.

That said, I can't find the source right now but I believe the quote is something along the lines a sizable percentage of Firefox's security bugs would be less severe or nonexistent in Rust vs. C++.