Can't Enable Comments On Custom Post Types

How can I enable comments on custom post types?

I’m on a fresh install of WP 3.0 with no plugins installed.
This is the code I have for a custom post type:

register_post_type("product", array(
	"label" 	        => __("Products"),
	"singular_label" 	=> __("Product"),
	"public" 		=> true,
	"capability_type"       => "post",
	"hierarchical"		=> false,
	"rewrite"		=> array("slug" => "Shop"),
	"query_var"		=> false,
	"show_ui"		=> true,
	"supports"		=> array("title", "editor", "thumbnail", "author", "custom-fields", "comments")
));

And I’m using the default comment template provided by wordpress, without any custom callback:

<?php comments_template(); ?>

I have also checked ‘allow comments’ under ‘Discussion’ for this post type.