Ok, I don’t know why, but it’s working as expected now.
It must have been a cache issue, but I swear I was clearing the cache regularly.
For the sake of closure, here’s the code that worked (once the field was accessible):
<section class="center-align stories" id="stories">
<div class="wrap cf">
<div class="row">
<?php
if (have_posts()) : while (have_posts()) : the_post();
$my_id = get_the_ID();
?>
<?php // Only show posts where 'visibile_on_index' is not 0 (either 1 or unset)
if (get_post_field('visible_on_index', $my_id) != 0) { ?>
<div class="fourth <?php foreach(get_the_category() as $cat){ echo ' '.$cat->slug; }?>">
<div class="inner">
<a href="<?php the_permalink(); ?>" class="img-holder" style="background-image: url(<?php the_post_thumbnail_url('full'); ?>)"></a>
<a href="<?php the_permalink(); ?>">
<h4><?php the_title(); ?></h4>
</a>
<?php the_excerpt(); ?>
</div>
</div>
<?php }; ?>
<?php endwhile; ?>
<?php bones_page_navi(); ?>
<?php endif; ?>
</div>
</div>
</section>
