In html_api.php this code:
if ( !$t_readonly ) {

UPDATE button

        echo '<td class="center">';
        html_button_bug_update( $p_bug_id );
        echo '</td>';

        # ASSIGN button
        echo '<td class="center">';
        html_button_bug_assign_to( $p_bug_id );
        echo '</td>';

    }

    # Change State button
    echo '<td class="center">';
    html_button_bug_change_status( $p_bug_id );
    echo '</td>';

and user can change noneditable task (closed).
If this change to this:

    if ( !$t_readonly ) {
        # UPDATE button
        echo '<td class="center">';
        html_button_bug_update( $p_bug_id );
        echo '</td>';

        # ASSIGN button
        echo '<td class="center">';
        html_button_bug_assign_to( $p_bug_id );
        echo '</td>';

        # Change State button
        echo '<td class="center">';
        html_button_bug_change_status( $p_bug_id );
        echo '</td>';

    }

All work fine!