We have the same problem. However it works fine on our staging site (a subdomain). I don't have access to the Apache error logs to see what error is reported. The terms.php files are identical on both sites, and have the same permissions.
Yes, the /com_dtregister directory and levels above must be 755 permission and the files inside 644. This is standard permissions on most servers. Using the latest DT Register, the terms window will often times work even without the correct permissions setting, but anyone having this issue must correct permissions.