There is no requirement to post fitness minutes to facebook and the preference to check the box to share or not is an option in your account/email preferences. You can get to that from your Start page. Once you click on the account/email preference link, click on the community tab, make your selections, and save your changes.
Checking or unchecking the box doesn't impact your ability to track minutes on the site. Can you please describe what happens when you try to track fitness that makes it appear you are unable to enter your minutes?