How to hide media uploads by other users in the Media menu?

Actually you can, and here’s how to do it:

This code hides all posts and media that do not belong to the currently logged in author (you can change it to apply to other user roles). It also fixes the post and media count on the filter bars (e.g. All | Images | Videos | Unattached).

// Show only posts and media related to logged in author
add_action('pre_get_posts', 'query_set_only_author' );
function query_set_only_author( $wp_query ) {
    global $current_user;
    if( is_admin() && !current_user_can('edit_others_posts') ) {
        $wp_query->set( 'author', $current_user->ID );
        add_filter('views_edit-post', 'fix_post_counts');
        add_filter('views_upload', 'fix_media_counts');
    }
}

// Fix post counts
function fix_post_counts($views) {
    global $current_user, $wp_query;
    unset($views['mine']);
    $types = array(
        array( 'status' =>  NULL ),
        array( 'status' => 'publish' ),
        array( 'status' => 'draft' ),
        array( 'status' => 'pending' ),
        array( 'status' => 'trash' )
    );
    foreach( $types as $type ) {
        $query = array(
            'author'      => $current_user->ID,
            'post_type'   => 'post',
            'post_status' => $type['status']
        );
        $result = new WP_Query($query);
        if( $type['status'] == NULL ):
            $class = ($wp_query->query_vars['post_status'] == NULL) ? ' class="current"' : '';
            $views['all'] = sprintf(__('<a href="https://wordpress.stackexchange.com/questions/30308/%s"'. $class .'>All <span class="count">(%d)</span></a>', 'all'),
                admin_url('edit.php?post_type=post'),
                $result->found_posts);
        elseif( $type['status'] == 'publish' ):
            $class = ($wp_query->query_vars['post_status'] == 'publish') ? ' class="current"' : '';
            $views['publish'] = sprintf(__('<a href="https://wordpress.stackexchange.com/questions/30308/%s"'. $class .'>Published <span class="count">(%d)</span></a>', 'publish'),
                admin_url('edit.php?post_status=publish&post_type=post'),
                $result->found_posts);
        elseif( $type['status'] == 'draft' ):
            $class = ($wp_query->query_vars['post_status'] == 'draft') ? ' class="current"' : '';
            $views['draft'] = sprintf(__('<a href="https://wordpress.stackexchange.com/questions/30308/%s"'. $class .'>Draft'. ((sizeof($result->posts) > 1) ? "s" : "") .' <span class="count">(%d)</span></a>', 'draft'),
                admin_url('edit.php?post_status=draft&post_type=post'),
                $result->found_posts);
        elseif( $type['status'] == 'pending' ):
            $class = ($wp_query->query_vars['post_status'] == 'pending') ? ' class="current"' : '';
            $views['pending'] = sprintf(__('<a href="https://wordpress.stackexchange.com/questions/30308/%s"'. $class .'>Pending <span class="count">(%d)</span></a>', 'pending'),
                admin_url('edit.php?post_status=pending&post_type=post'),
                $result->found_posts);
        elseif( $type['status'] == 'trash' ):
            $class = ($wp_query->query_vars['post_status'] == 'trash') ? ' class="current"' : '';
            $views['trash'] = sprintf(__('<a href="https://wordpress.stackexchange.com/questions/30308/%s"'. $class .'>Trash <span class="count">(%d)</span></a>', 'trash'),
                admin_url('edit.php?post_status=trash&post_type=post'),
                $result->found_posts);
        endif;
    }
    return $views;
}

// Fix media counts
function fix_media_counts($views) {
    $_total_posts = array();
    $_num_posts = array();
    global $wpdb, $current_user, $post_mime_types, $avail_post_mime_types;
    $views = array();
    $count = $wpdb->get_results( "
        SELECT post_mime_type, COUNT( * ) AS num_posts 
        FROM $wpdb->posts 
        WHERE post_type="attachment" 
        AND post_author = $current_user->ID 
        AND post_status != 'trash' 
        GROUP BY post_mime_type
    ", ARRAY_A );
    foreach( $count as $row )
        $_num_posts[$row['post_mime_type']] = $row['num_posts'];
    $_total_posts = array_sum($_num_posts);
    $detached = isset( $_REQUEST['detached'] ) || isset( $_REQUEST['find_detached'] );
    if ( !isset( $total_orphans ) )
        $total_orphans = $wpdb->get_var("
            SELECT COUNT( * ) 
            FROM $wpdb->posts 
            WHERE post_type="attachment" 
            AND post_author = $current_user->ID 
            AND post_status != 'trash' 
            AND post_parent < 1
        ");
    $matches = wp_match_mime_types(array_keys($post_mime_types), array_keys($_num_posts));
    foreach ( $matches as $type => $reals )
        foreach ( $reals as $real )
            $num_posts[$type] = ( isset( $num_posts[$type] ) ) ? $num_posts[$type] + $_num_posts[$real] : $_num_posts[$real];
    $class = ( empty($_GET['post_mime_type']) && !$detached && !isset($_GET['status']) ) ? ' class="current"' : '';
    $views['all'] = "<a href="upload.php"$class>" . sprintf( __('All <span class="count">(%s)</span>', 'uploaded files' ), number_format_i18n( $_total_posts )) . '</a>';
    foreach ( $post_mime_types as $mime_type => $label ) {
        $class="";
        if ( !wp_match_mime_types($mime_type, $avail_post_mime_types) )
            continue;
        if ( !empty($_GET['post_mime_type']) && wp_match_mime_types($mime_type, $_GET['post_mime_type']) )
            $class=" class="current"";
        if ( !empty( $num_posts[$mime_type] ) )
            $views[$mime_type] = "<a href="upload.php?post_mime_type=$mime_type"$class>" . sprintf( translate_nooped_plural( $label[2], $num_posts[$mime_type] ), $num_posts[$mime_type] ) . '</a>';
    }
    $views['detached'] = '<a href="upload.php?detached=1"' . ( $detached ? ' class="current"' : '' ) . '>' . sprintf( __( 'Unattached <span class="count">(%s)</span>', 'detached files' ), $total_orphans ) . '</a>';
    return $views;
}