“Unfortunately BulletProof Security plugin is causing this issue. It is changing WordPress files that make it impossible to use any other backup solution besides the one they provide.”
You can use any other backup plugins or any other plugins with BPS Pro. BPS Pro does not prevent other backup plugins from working along with BPS Pro DB Backup or prevent any other plugins from doing whatever they do. I suspect that the problem is related to AutoRestore/Quarantine, but could be related to more than just ARQ. AutoRestore/Quarantine is an IDPS File Monitor that monitors all of your website files for changes. See the links below for best procedural steps for cloning sites and also the AutoRestore/Quarantine Guide so that you have a complete understanding of all the factors involved in cloning a site. And yep it may just be simpler these days to turn all security off in the site you want to clone or just uninstall BPS Pro and then run the Setup Wizard again on the site used to clone and any new sites that you are creating with that clone.
Note: If the Backup Creator plugin stores its backup files under the /wp-content folder then you will need to create an AutoRestore folder Exclude rule for that backup folder so that AutoRestore does not check that backup folder or you can change the backup folder path to any folder name under the /wp-content/bps-backup/ folder, which is already excluded from being checked by AutoRestore and the /bps-backup/ folder has security protection so that all files under the /bps-backup/ folder are protected.
Note: If you have used the BPS Pro DB Table Prefix Changer to change the name of your database table prefix name then be sure to check that your wp-config.php file also has the same db table prefix name. Also if you are importing a database that has db tables with a different db table prefix other than the default wp_ db table prefix and the default WordPress db tables already exist in that database then you will have 2 sets of db tables, but the only db tables that will be used will be whatever db table prefix you set in your wp-config.php file. In this scenario you can delete all db tables with the wp_ db table prefix name since they are not be used and the are duplicate db tables.
http://forum.ait-pro.com/forums/topic/migrating-moving-or-cloning-websites/
http://forum.ait-pro.com/forums/topic/autorestore-quarantine-guide-read-me-first/
http://forum.ait-pro.com/video-tutorials/#autorestore-quarantine