To start with, it does not rely on any third party service, though the main engine is based off of HotSpot Shield's. Since it's part of BitDefender's software, it does not have access to logs, nor the personal browsing history. Still, it does collect information, but basic anonymous data: performance related, issue/crashes related.
It depends entirely on you wether to trust or not a security company that (probably) has ties with numerous governments in order to combat cybercrime to protect your personal information.