Sudo Logins Not Working

In the Webmin Users module, under Unix User Authentication, the option to "Allow users who can run all commands via sudo to login as root" does not seem to work. If I select this option and attempt to login with my regular user account, login is denied. This should confirm that I have sudo access:

# echo password | su user -c 'sudo -l -S'
User user may run the following commands on this host:
(ALL) ALL

If I select the option "Allow Unix users listed below to login ..." and explicitly enter my username, then it does work as expected. However, I think it should work for all sudoers without having to enter their usernames here.