What they want to do is install WordPress for you and transfer all of your content over to them.
You will then be using WordPress.org, not WordPress.com.
We do not provide database access, but once WordPress is installed, you can move your content following this guide: http://en.support.wordpress.com/moving-a-blog/#moving-to-wordpress-org
To clear up any confusion, WordPress.com and WordPress.org are two different entities.
http://support.wordpress.com/com-vs-org/
WordPress.org has complete support and documentation sites for self-hosted/installed versions of WordPress at:
http://wordpress.org/support/
http://codex.wordpress.org/
We do offer yearly and one-time premium support packages for self-hosted WordPress sites through our VIP program, available at http://vip.wordpress.com