"global groups" aren't global in multisite with subdomains

I’m testing some things with W3 Total Cache 0.9.2.4 in a WordPress 3.4.2 multisite installation with subdomains.

I try to use the default global group “global-posts” to show the latest posts from blog_id == 1 on every child blog via object caching.

But, the generated key differs on each blog_id. So it seems to be impossible to cache objects once for the whole network.

The reason seems to be, that _get_cache_key in ObjectCache.php uses the $host to generate a key:

$host = w3_get_host();
if (in_array($group, $this->global_groups)) {
    $host_id = $host;
} else {
    $host_id = sprintf('%s_%d', $host, $blog_id);
}

But, the host contains the subdomain like “www.example.com” and “blog57.example.com”. So the generated key differs on every blog_id.

Am I missing something? Can someone confirm this?

http://wordpress.org/extend/plugins/w3-total-cache/