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):

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

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