Not sure exactly how you're Exporting (are you trying to 'Share' to these services via FCP7?) but it may be due to the system-wide account settings that Mountain Lion uses; if you go to the System Prefs, you'll see under 'Mail, Contacts & Calendars' that you can log in to various services there so that they're available to all applications.
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SCQT! Self-contained QuickTime ? pass it on!