In this situation a full backup was not possible to truncate the logs. Symantec Backup Exec was still backing up the databases every night though.
To cure this problem, a quick little fix:
1. Open up Microsoft SQL Server Management Studio
2. New Query
3. Type in the following and press execute:
ALTER DATABASE[SharePoint_Config] SET RECOVERY SIMPLE WITH NO_WAIT
DBCC SHRINKFILE ('SharePoint_Config_Log')