The idea of bootstrapping is that you start with nothing, or at least with almost nothing. In case of stage0 (the first stage of live-bootstrap) this a small program that converts a file with hexadecimal characters (in pairs) to a binary file. From there you have to build everything. To compile Rust, you need a Rust or C compiler, I understand. I have no idea how hard it would be to build a minimal Rust compiler that could compile itself, one that not necessary performs all the checks that the (full) Rust compiler would do.

I think that Rust is build as part of live-bootstrap, but at a much later stage when the latest version of the GNU C compiler has been build.