The /etc/shadow (or equivalent) file must be owned by root.
The /etc/shadow file contains the list of local system accounts. It is vital to system security and must be protected from unauthorized modification. Failure to give ownership of sensitive files or utilities to root or bin provides the designated owner and unauthorized users with the potential to access sensitive information or change the system configuration which could weaken the system's security posture.
How this relates to the STIG checklist: STIG vs SCAP benchmark.