Most of the code in my Linux distro is written in C, yet I don't see many segfaults or data corruption in my favorite tools, even those exposed to the internet. It just works. Supposed buffer overflows and double-frees don't affect me daytoday despite 95%+ code I run being written in C, "catastrophic" issues like heartbleed notwithstanding.
People make mistakes, sure. They'll make them with "safe" languages, too. Rust programs are not immune from mistakes. They'll just be of a different kind.
PHP is memory safe, and there were many easily exploited (not just exploitable) vulnerabilities in software written with PHP. (and it doesn't even have escape hatches out of its memory safety)
