Warnings still show on page even after setting Error messages to None in Logging and Errors
That's a pretty specific error message, and google says it is coming from this module:

https://www.drupal.org/project/netforum

at these lines: 808-812

  catch (Exception $e) {
    if (isset($cache_max)) { //this implies that we went even further back in the cache and could not connect, so call it quits
      if (variable_get('netforum_hide_error_messages', 0) == 0 || user_access('administer site configuration')) {
        drupal_set_message(t('Could not retreive data from server or cache.'), 'error');
      }


More specifically to your question, because the above module is using drupal_set_message it is not going to be effected by the 'error_reporting' level since that only impacts errors that would go to the logs. This makes sense as you would want to be able to suppress syntax or PHP errors while still letting system messages like "node was saved" or "subscription processed" still appear to the screen. 

Your options to suppress this are to deal with the underlying cause of the error from the module (best case), or remove the 'messages' functionality from your theme, i.e. remove where ever it is that it says:

print $messages;


but again, that is probably not the best course of action here.