The claim I've heard (and I think also made) is a bit different from that. It's more like: "dealing with memory corruption issues isn't a significant portion of the debugging effort in [idiomatic] C++ code". i.e. the claim is not that you somehow won't run into them; rather, the claim is that they form a small fraction of the actual bugs you run into (either count-wise or time-wise), if you're writing C++ "properly". (If I had to make up a number, I'd say < 5%.)
This obviously isn't to say memory safety isn't an issue, or that security is a negligible property. Rather, it's to point out that most issues are of a different kind, and if you think that memory safety will decrease your workload significantly, that's unlikely to be the case if you're writing C++ with the correct idioms.
I think this response is usually in response to claims about how (say) a language like Rust results in N times faster development than C++. If that's truly the case, it's unlikely to be due to memory safety per se, but due to other factors.