I haven't heard this one before. It sounds almost like it's not reading the site collection setting for review membership requests, and just pulling the default value of false.
Is the membership request web part being added to a page in the same site collection that you've set the 'Review Membership Requests' value? For a test, add a new membership request web part to a page on the root site of the site collection, and see if that
Also, I assume you can view the Site Membership Review List (From the FBA Membership Request Management link in Site Settings)? If the above doesn't work, you may want to try deactivating + activating the feature in the site collection features. This
will drop and recreate the Site Membership Review List.
Check that you're running the latest version (1.3.1) from the FBA Site Configuration page.
If all of the above doesn't work, create a user with the membership request web part and then check the SharePoint logs to see if anything is mentioned in there. You can search for 'FBA Pack' to see if the FBA Pack itself has logged any errors.