There were a few days after initial rollout where rustc-src was corrupt. What does rustc -Vv say? If it's old I'd suggest upgrading with rustup update nightly first.
I don't see this error locally on the most recent nightly.
Strange: I reinstalled yesterday everything with rustup, because I reainstalled Linux, but with the same home directory. And somehow rustup show pointed to an old nightly build. I removed it and now it works.
This also happened to me on a Windows platform with an Antivirus software enabled. I turned off an Antivirus, but rustup still refused to install rust-src component. It installed successfully, when only I had to manually delete the src directory.