Behold, good sir, follow these steps to verify that Joomla is setup good and well for full SQL access:
1) In the Joomla backend, head over to 'Global Configuration', go to the third tab 'Server'
2) Box on the top right, make a note of the 'Database Settings'. They should be something like this as an example:
Database Type : mysql
Hostname : localhost
Username : jonusc_root
Database : jonusc_main
Database Prefix : jos_
...you can ignore the top one (Database Type) and the last one (Prefix), just make note of Hostname - it should probably always be localhost unless you have exotic server settings (if it's not localhost, let me know as it may be the issue - your server could be using some kind of route/proxy or shared database. The Username and database, write them down.
3) Go to phpmyadmin now, and on the left click the database name you got from step 2 (in my case, I click "jonusc_main"
4) Now in phpmyadmin, click the 'Prilileges' tab - it should be the second last one. Verify the permissions there; in my case this is how it should look:
User Host Type Privileges Grant Action
jonusc_root localhost global ALL PRIVILEGES Yes Edit Privileges
{Probably some more, such as root, dont worry about them just make sure any "root" account is on "ALL PRIVILEGES" as they should be}
If everything there is correct, then perhaps there may be an issue with the database. Or there is a bug in JoomlaComment we havn't yet seen
Don't worry about it too much now, but if you have strange things happen in future for a different extension, lodge a support ticket to your webhost and mention that you had trouble with a database operation once before.