Rust was adopted at Dropbox for some serving infrastructure use cases more than a year before the sync rewrite was started, which was about four years ago. I'd say we solidly predated the "rewrite it in Rust" meme.
I believe that this rewrite was only successful because of Rust's ability to both interact safely/efficiently with underlying OS APIs (they're pretty much all C-like) and to encode complex concepts into the type system and the compiler. Rust isn't the only language with these properties, but it is one of the few -- and it's one that we really enjoyed using.