This is almost certainly incorrect unless you're running a very, very old RHEL/CentOS release. I believe /var/lib/ntp is the canonical directory for the drift file in 4.x and 5.x. I doubt ntpd is allowed to write to /etc/ntp, especially if SELinux is enabled.
Good observation, Paul. That configuration is in fact from an ancient version of Red Hat which I plan to upgrade this week.
Have you tried shutting down ntpd and relaunching it manually with the "don't fork and give me lots of debugging output" switches (-n -ddd) enabled?
Alternatively (or additionally), you might try wrapping ntpd in strace to see if any system calls are being thwarted.
I learned today that our ISP is blocking UDP traffic. I am going to ask them to make an exception for port 123 to fix this.