Change the disabled status of a form element via Ajax
I found the solution here:

Enable DropDown using Ajax Call

The code finally gets this:

     function hook_models_update($form, &amp;$form_state) {
         unset($form_state['input']['model'], $form_state['values']['model']);
         $brand = $form_state['values']['brand'];
         $form['model']['#autocomplete_path'] = 'providers/autocomplete/' . $brand;
         unset($form['model']["#attributes"]['disabled']);
         $form['model']['#disabled'] = FALSE;
         return form_builder($form['#id'], $form['model'], $form_state);
} // function


The trick lies in these two lines:

     unset($form['model']["#attributes"]['disabled']);
     $form['model']['#disabled'] = FALSE;


Apparently, there has to be an unset and not of #disabled, but #attributes - disabled. Why this is so convoluted is beyong my comprehension.