"Edit media" permission allows editing other users' media?

Hello,

It seems that users need the "Edit media" permission in order to use the media popup. Otherwise the popup opens but is empty (please see screenshot).
The problem is that "Edit media" permission seems to also enable users to edit other users' media.

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So my questions are:
- Am I missing something regarding the media and media-gallery set of permissions
- If the answer is no, could you please give your opinion/advise on the following workaround :

1) in a costum module, change the menu item 'media-gallery/detail/%node/%media/edit' so that it uses another access callback function

<?php
function mymodule_menu_alter(&$items) {
  $items['media-gallery/detail/%node/%media/edit'] = array(
    'title' => 'Edit',
    'page callback' => 'media_gallery_media_page_edit',
    'page arguments'  => array(2, 3),
    'access callback' => 'media_gallery_media_access',	// change here
    'access arguments' => array('edit', 2),				// change here
    'weight' => 0,
    'type' => MENU_LOCAL_TASK,
    'context' => MENU_CONTEXT_PAGE | MENU_CONTEXT_INLINE,
    'file' => 'media_gallery.pages.inc',
    'theme callback' => '_node_custom_theme',
  );
}
?>

2) Give access to media if user has "Edit media" permission AND if user is author of gallery:

<?php
function media_gallery_media_access($op, $node) {
	global $user;
	return media_access($op) && $user == $node->uid;
}
?>

Thanks in advance.