That is provably false:
https://www.joelonsoftware.com/2000/04/06/things-you-should-...
There are numerous developers on this forum who could provide eyewitness accounts of project rewrite horror stories.
The same thing would happen if you rewrote in rust.
However, there are some patterns that Rust does not allow that other languages do allow which may help to avoid problems.
For example, creating cyclic dependencies and relationships is more difficult in Rust due to the way that ownership rules are enforced. Rust also helps to avoid data races and memory unsafety issues so that whole classes of errors and bugs can be avoided.
You're confusing things. Google's example focused on rewriting specific components with a specific goal in mind: fix/avoid unsafe memory access. The examples in that blog post consist of major rewrites of huge software projects like browsers, whose goal was to be feature complete.
Those are quite different things.
The statement, "Almost every project sees fewer issues with a rewrite, no matter which languages are involved.", was too broad and I wanted to show how I disagreed with it when the article I cited was concerned with component rewrites.
I did not intend to conflate the two since the scopes are quite different.