I had problems with the following combination :
Drupal + Drupal HybridAuth + Drupal OAuth + HybridAuth because OAuthConsumer class is already provided within Drupal OAuth.
=> Callback from linkedin and twitter lead to this error message :
PHP Fatal error: Cannot redeclare class OAuthConsumer in /var/www/sites/domain/sites/all/modules/oauth/lib/OAuth.php on line 20
@see : https://www.drupal.org/node/2147429
Require OAuth.php only if not exist
Not a HybridAuth issue since the issue is caused by incompatibility with another Drupal module, but since this could help others as well I'll allow this in.