Alright, we found it. On our test site with PHP 5.1 we hadn't installed JomSocial yet. When we did, WHAMO.
Anyone affected, please try the following and post your results. This fixed it immediately for us. It's a combination of both JomSocial and FBConnect check to see which version of PHP your using (and whether the JSON library needs to be included). However, they check in slightly different and conflicting ways.
In /administrator/components/com_jfbconnect/assets/facebook-api/jsonwrapper/jsonwrapper_inner.php on lines 4/5, add the following bolded line:
if (!defined('SERVICES_JSON_SLICE'))
require_once 'JSON/JSON.php'; # <--- this line should already be there
There is another post about another issue with this file below that we'd recommend implementing now as well (while your there):
<!-- m --><a class="postlink" href="
www.cmsmarket.com/forum/index.php?f=38&t...&rb_v=viewtopic#p413">
www.cmsmarket.com/forum/index.ph ... topic#p413
Please let us know how these 2 changes go. Both will be included in the upcoming 2.0.1 release.