I sent you a PM with example URLs to test from your Facebook fan page. The Hostgator tech was able to reproduce the 403 with these URLs from his test FB page. Consequently, when he deactivated BPS, there were no more 403 errors in FB.
We don’t have any active FB or social media plugins. The WP Theme we use (Max mag) comes with social widgets. The ones we use are the facebook like box with faces, and the floating social media share bar. To my knowledge, there is no interaction between these widgets and the action of posting a link in our FB page, since you can post any link from any site.
Try to post the links I PMed you in your FB page, see what you get…