Scott,
Obviously, that shouldn't be happening. There's an easy fix, provided below, and we'll also do more investigation to see what is making the problem appear on your site when we haven't seen or heard of this on others.
Either way, in the /plugins/user/jlinkeduser/jlinkeduser.php file, at line 35, you'll see the following:
$jLinkedLibrary = JLinkedApiLibrary::getInstance();
Update that with the additional line below:
require_once JPATH_ROOT . DS . 'components' . DS . 'com_jlinked' . DS . 'libraries' . DS . 'linkedin.php';
$jLinkedLibrary = JLinkedApiLibrary::getInstance();
That should fix you right up, and sorry for the troubles.
Thanks,
Alex