I think it makes a good point that some of the difference here is just perception due to dependencies in C/C++ being less immediately visible since they're dynamically loaded. To some degree that is a plus though as you likely trust the maintainers of your OS distribution to provide stable, supported libraries.
As other commenters have said, perhaps this is an area where the Rust maintainers could provide some kind of extended standard library where they don't guarantee backwards compatibility forever, but do provide guarantees about ongoing fixes for security issues.