That wiki article seems to define memory-safe code as not containing an arbitrary list of bugs. This doesn't really make sense because even if you have code that doesn't contain those bugs, and even if you have a compiler that helps you to find those bugs, programming is always unsafe. You are not safe just because you don't use the "unsafe" keyword in Rust.
The list isn't arbitrary. Bugs that let you read and write different memory than you meant to are some of the easiest to exploit. If you look back at the type of bugs that make headlines, they're pretty much all memory safety issues or code injection (and the memory issues show up more often).
