Of course, dependency-reliance falls on a spectrum for any individual programmer. On the one hand you have script kiddies with 400 npm dependencies gathered from arcane Discord channels - on the other you have old bearded wizards who don't understand why you'd need printf() when you can just mov rax 1; syscall.
I find Rust is not strongly opinionated about this. You can just as easily eschew dependencies as use them. There's usually a good array of options available, or you could always FFI to a C lib directly if you need to.