Can't connect with ssh and sshd complains about permissions on authorized_keys files

I was recently trying to connect to a CentOS box from Windows and had the following error in /var/log/secure (after enabling DEBUG3 level logging in /etc/ssh/sshd_config):

Dec 19 18:01:05 hostname sshd[25119]: debug1: trying public key file /root/.ssh/authorized_keys
Dec 19 18:01:05 hostname sshd[25119]: debug1: Could not open authorized keys '/root/.ssh/authorized_keys': Permission denied

It's an SELinux problem, and I don't quite understand it, but here's the one-liner that fixes it:

restorecon -FRvv ~/.ssh

Found on stackoverflow: "SSHD Gives error could not open Authorized Keys, although permissions seem correct"