The method DataExporter.encodeParentAndChildrenAsString(FacesContext fc, UIComponent uic) indirectly calls the toString method of a value instead of using a converter.
The problem is situated at this line: str.append(value).

Current implementation:

private String encodeParentAndChildrenAsString(FacesContext fc,
            UIComponent uic) {
        StringBuffer str = new StringBuffer();
        Object value = uic.getAttributes().get("value");
        if (value != null)
            str.append(value);
        else {
            ValueBinding vb = uic.getValueBinding("value");
            if (vb != null)
                str.append(vb.getValue(fc));
        }

        if (uic.getChildCount() > 0) {
            Iterator iter = uic.getChildren().iterator();
            while (iter.hasNext()) {
                UIComponent child = (UIComponent) iter.next();
                str.append(encodeParentAndChildrenAsString(fc, child));
            }
        }
        return str.toString();
    }

I think that it would be necessary to change this method with an implementation like this:

private String encodeParentAndChildrenAsString(FacesContext fc,
            UIComponent uic) {
        StringBuffer str = new StringBuffer();
        Object value = uic.getAttributes().get("value");
        if (value != null) {
         Converter converter = null;
         if(uic instanceof UIOutput) {
         converter = ((UIOutput)uic).getConverter();
         }
         if(converter == null) {
         converter = FacesContext.getCurrentInstance().getApplication().createConverter(value.getClass());
         }
         if(converter != null) {
         str.append(converter.getAsString(FacesContext.getCurrentInstance(), uic, value));
         } else {
         str.append(value);
         }
        }
        else {
            ValueBinding vb = uic.getValueBinding("value");
            if (vb != null)
                str.append(vb.getValue(fc));
        }

        if (uic.getChildCount() > 0) {
            Iterator iter = uic.getChildren().iterator();
            while (iter.hasNext()) {
                UIComponent child = (UIComponent) iter.next();
                str.append(encodeParentAndChildrenAsString(fc, child));
            }
        }
        return str.toString();
    }