How To Fix WP Query Returns Results But Shouldn’t?

Couple of things to consider here:

1.) Try adding the meta query only if the value is present:

$pairedThing = get_field('myThing');
$args = [
    'posts_per_page' => 2,
    'post_type'      => 'thing',    
];
if ( ! empty( $pairedThing ) ) {
    $args['meta_key']   = 'identifier';
    $args['meta_value'] = $pairedThing;
}

2.) Account for posts without the meta-key set:

$pairedThing = get_field('myThing');
$args = [
    'posts_per_page' => 2,
    'post_type'      => 'thing',
    'meta_query'     => [
        'my_meta_query' [ // Multiple meta-queries per handle.
            'relation' => 'OR',
            [
                'key'     => 'identifier',
                'value'   => $pairedThing,
                'compare' => '=',
            ],
            [
                'key'     => 'identifier',
                'compare' => 'NOT EXISTS',
            ],
        ],
    ]
];