The register_post_type() function takes a post type name as argument for map_meta_cap, where the default is post. Take a look at the internals of get_post_type_capabilities() for extended insights. That should help you to understand how it’s meant to be:
function get_post_type_capabilities( $args ) {
if ( ! is_array( $args->capability_type ) )
$args->capability_type = array( $args->capability_type, $args->capability_type . 's' );
// Singular base for meta capabilities, plural base for primitive capabilities.
list( $singular_base, $plural_base ) = $args->capability_type;
$default_capabilities = array(
// Meta capabilities
'edit_post' => 'edit_' . $singular_base,
'read_post' => 'read_' . $singular_base,
'delete_post' => 'delete_' . $singular_base,
// Primitive capabilities used outside of map_meta_cap():
'edit_posts' => 'edit_' . $plural_base,
'edit_others_posts' => 'edit_others_' . $plural_base,
'publish_posts' => 'publish_' . $plural_base,
'read_private_posts' => 'read_private_' . $plural_base,
);
// Primitive capabilities used within map_meta_cap():
if ( $args->map_meta_cap ) {
$default_capabilities_for_mapping = array(
'read' => 'read',
'delete_posts' => 'delete_' . $plural_base,
'delete_private_posts' => 'delete_private_' . $plural_base,
'delete_published_posts' => 'delete_published_' . $plural_base,
'delete_others_posts' => 'delete_others_' . $plural_base,
'edit_private_posts' => 'edit_private_' . $plural_base,
'edit_published_posts' => 'edit_published_' . $plural_base,
);
$default_capabilities = array_merge( $default_capabilities, $default_capabilities_for_mapping );
}
$capabilities = array_merge( $default_capabilities, $args->capabilities );
// Post creation capability simply maps to edit_posts by default:
if ( ! isset( $capabilities['create_posts'] ) )
$capabilities['create_posts'] = $capabilities['edit_posts'];
// Remember meta capabilities for future reference.
if ( $args->map_meta_cap )
_post_type_meta_capabilities( $capabilities );
return (object) $capabilities;
}
A better way to debug that is the following hook:
do_action( 'registered_post_type', $post_type, $args );
Use it like this (it runs exactly after registration):
add_action( 'registered_post_type', function( $cpt, $args )
{
$cpt === 'your_cpt_name' && var_dump(
$args->capability_type,
$args->cap // result of get_post_type_capabilities()
);
}, 10, 2 );
Replace your_cpt_name with your actual name that you used as 1st arg during registration.
Also keep in mind that for most use cases, it’s completely unnecessary to check against custom capabilities. Those are much harder to maintain that it should be. I prefer checking against the post type and a default capability instead.