a programatically created non-standard webform node is not initialized properly

Tried this on a clean 7.21 install with webform 7.x-4.0-alpha6 and 7.x-3.18

When I write a function to create a node from a webform-enabled node type ( say, 'page' ), the webform components are not initialized properly: they are not displayed when viewing the node.
The component editor is also empty, but if I add a component, it yields this error:

PDOException: SQLSTATE[23000]: Integrity constraint violation: 1062 Duplicate entry '3-1' for key 'PRIMARY': INSERT INTO {webform_roles} (nid, rid) VALUES (:db_insert_placeholder_0, :db_insert_placeholder_1); Array ( [:db_insert_placeholder_0] => 3 [:db_insert_placeholder_1] => 1 ) in webform_node_insert() (line 1135 of /usr/www/users/name/sites/all/modules/webform/webform.module).

However, if I change the node type to 'webform' in my function, everything works.

Below is a sample implementation that creates a node of type 'page' and attaches a webform to it.

 //assemble basic webform node
 $node = new stdClass();
 $node->type = 'page'; //change to webform to work
 node_object_prepare($node);
 
 $node->title = 'Example webform';
 $node->language = 'en';
 
 node_save($node);
 
 //if node creation was successful, create webform
 if ($nid = $node->nid) {
  
  //define webform settings
  $node->webform = array();
  $node->webform['nid'] = $nid;
  $node->webform['confirmation'] = '';
  $node->webform['confirmation_format'] = 'full_html';
  $node->webform['redirect_url'] = '<none>';
  $node->webform['status'] = '1';
  $node->webform['block'] = '0';
  $node->webform['teaser'] = '0';
  $node->webform['allow_draft'] = '0';
  $node->webform['auto_save'] = '0';
  $node->webform['submit_notice'] = '0';
  $node->webform['submit_text'] = 'Test';
  $node->webform['submit_limit'] = '-1';
  $node->webform['submit_interval'] = '-1';
  $node->webform['total_submit_limit'] = '-1';
  $node->webform['total_submit_interval'] = '-1';
  $node->webform['record_exists'] = true;
  $node->webform['roles'] = array('1');
  
  //define webform components
  $node->webform['components'] = array();
  $node->webform['emails'] = array();
  $node->webform['conditionals'] = array();
  
  $cid = 1;
  
  //define example textfield
  $node->webform['components'][$cid] = array();
  $node->webform['components'][$cid]['nid'] = $nid;
  $node->webform['components'][$cid]['cid'] = '' . $cid;
  $node->webform['components'][$cid]['pid'] = '0';
  $node->webform['components'][$cid]['form_key'] = 'example_field';
  $node->webform['components'][$cid]['name'] = 'Example field';
  $node->webform['components'][$cid]['type'] = 'textfield';
  $node->webform['components'][$cid]['value'] = '';
  $node->webform['components'][$cid]['mandatory'] = '0';
  $node->webform['components'][$cid]['weight'] = '' . $cid;
  $node->webform['components'][$cid]['page_num'] = 1;
  $node->webform['components'][$cid]['extra'] = array();
  $node->webform['components'][$cid]['extra']['title_display'] = 'before';
  $node->webform['components'][$cid]['extra']['private'] = 0;
  $node->webform['components'][$cid]['extra']['disabled'] = 0;
  $node->webform['components'][$cid]['extra']['unique'] = 0;
  $node->webform['components'][$cid]['extra']['width'] = '';
  $node->webform['components'][$cid]['extra']['maxlength'] = '';
  $node->webform['components'][$cid]['extra']['field_prefix'] = '';
  $node->webform['components'][$cid]['extra']['field_suffix'] = '';
  $node->webform['components'][$cid]['extra']['description'] = '';
  $node->webform['components'][$cid]['extra']['attributes'] = array();
  
 }
 
 node_save($node);