If the binary still depends on libc.so.6 (glibc) at runtime, then it is not a fully static binary (read: not a static binary). It is a dynamically linked executable, albeit one where most non-libc dependencies have been statically linked.

I am not going to pretend I know Rust enough to comment (yes, would be a minute check), I was just commenting on the "Only libc is dynamically linked" bit.