You can disable tabs using a filter hook. Replace wpse_76095_isOurMediaUpload() with however you determine that you’re running the media popup.
add_filter('media_upload_tabs', 'wpse_76095_filterMediaUploadTabs');
/**
* filter out unwanted media upload tabs
* @param array $tabs
* @return array
*/
function wpse_76095_filterMediaUploadTabs($tabs) {
if (wpse_76095_isOurMediaUpload()) {
unset(
$tabs['type_url'], // no linking from external sites (no local image)
$tabs['gallery'], // no galleries
$tabs['nextgen'] // no NextGEN galleries
);
}
return $tabs;
}