Yes you are correct. In order to add your own theme you will have to move to WordPress.org. To clear up any confusion, WordPress.com and WordPress.org are two different entities. At WordPress.com, we provide hosting, support, and tons of features for blogs. Users also have the option to purchase a variety of upgrades to customize the look and feel of their blog. WordPress.org is a software for self-hosted sites. With WordPress.org, users are provided access to all backend files and can upload custom themes and plugins.
Check here to learn more about the difference between WordPress.com and WordPress.org:
We do offer tools for helping to make your WordPress.org experience as awesome as WordPress.com. Jetpack supercharges your website with features like easy video embedding, stats, and Twitter and Facebook sharing tools. VaultPress provides realtime, continuous backup and scans your website for security and performance. More information on both can be found at these links:
If you want to make the move to WordPress.org, this guide will step you through the process of moving your site to a WordPress.org instance:
As we only support sites hosted here at WordPress.com, all issues with the new site - including the importing of the file - must be taken to the WordPress.org support community:
If you'd like assistance moving your WordPress.com site to WordPress.org, we have a service called Guided Transfer that does all the work for you. Check it out to see if its right for you:
Feel free to reach out if you have any questions!