Hi Eliot,
My problem was that I was using the [value] in the template -which was returned from the key. Problem solved by using:
$field = get_field_object('selling_points');
$points = get_field('selling_points');
foreach ( $points as $point ){
$label = $field['choices'][ $point];
echo '<li class="bullet-item">'.$label.'</li>';
}
}
(My thanks to Micheal on your support staff)