this is frequently taken as axiomatic but there's no actual support for it in reality. there are plenty of healthy single-implementation languages (go, rust, scala, erlang) and plenty of unhealthy multi-implementation languages (c, d, sql, javascript) to go alongside the healthy/multi (python, ruby) and unhealthy/single (php, i guess, i don't care about this quadrant very much)
Why would that not be the case? crates.io is just a code repository like any other. You don't need crates.io to write/use Rust code, and crates.io has no specific requirement for a certain compiler.
It just so happens that currently only the main implementation of Rust language (rustc) can compile all of crates.io repository, but this could change in the future.