Ryan Hellyer on "Taxonomy bug"

I'm not sure if this is a bug in core or if I'm doing something wrong.

I have some code which generates a post-type called "Books" and I'm adding support for the post_tag taxonomy via register_taxonomy_for_object_type().

<?php

function test() {
	$args = array(
		'public' => true,
		'label'  => 'Books',
	);
	register_post_type( 'book', $args );

	register_taxonomy_for_object_type( 'post_tag', 'book' );
}
add_action( 'init', 'test' );

There are three posts in the book post-type:
http://uploads.ryanhellyer.net/random/2014/10/books-tags.png

Viewing the tags in the book post-type shows up all of the tags, including those from the posts post-type (note that the "Asten" tag indicates it has one post):
http://uploads.ryanhellyer.net/random/2014/10/books-tag.png

If I click on the Asten post tag, it displays no posts at all.
http://uploads.ryanhellyer.net/random/2014/10/books-tag-good.png

If I go to the posts post-type, the Asten post tag does show a post as expected:
http://uploads.ryanhellyer.net/random/2014/10/posts-tag.png

Question: Why does the "Asten" post tag display "1" when I'm on the book post-type? There is no post for the book post-type with a tag of "Asten" and so this should surely say "0" right? Clicking something which indicates there is one post, but it displaying zero does not make sense to me.