The "recent study" quoted in the article was published at the beginning of 2019, using older data.
Current vulnerability data shows that curl has very much limited the risk of memory safety issues. How many reported security vulnerabilities in the last two releases of curl? Zero so far. You have to go back 9 months before you find one expired-pointer derefence issue resulting in potential data being sent to the wrong connection in rare circumstances and configurations. Which is a logic error that could happen in Rust too.
To quote from a Oct 2020 study on Rust safety - "Our study results reveal that while Rust successfully limits the risks of memory-safety issues in the realm of unsafe code, it also introduces some side effects. In particular, most of the use-after-free and double-free bugs in our data set are related to the automatic drop scheme associated with the ownership-based memory management model." -- "Memory-Safety Challenge Considered Solved? An In-Depth Study with All Rust CVEs"
They study 60 Rust memory safety vulnerabilities.
As you can see not only does Rust not solve the memory safety problem, it has other issues. Additionally the old research quoted misleads people about the current status of reported memory safety issues in curl.
It also states that Rust completely prevents them - it does not. The article talks about mitigation, but also says: "would have been completely prevented by using a memory-safe language". The "completely prevented" claim in the article is the one not supported by current research. If you only read this article, you'd be mislead about memory safety in Rust.