I had an iMac which had the same issue.
This iMac is on OS X 10.8.5
Under Security & Privacy… The Require password ….. after sleep or screen saver begins was gray out.
This iMac was originally manage by Casper but has been removed already. There were some left over things that was stuck.
What I had to do was uncheck "Parental Controls". You'll need to do this with a different Admin account
- Log off the user that is having the issue
- Create a new admin account and log in with the new admin account.
- Select the user that has the "Require password" that is grayed out. Uncheck the "Enable Parental Controls" for that user.
- Log back onto the account that had the issue and you should be able to change the options to require password XX minutes after sleep or screen saver begins.
- This worked for me; hopefully this is useful for others out there.