Having the badge system work from a single point has a lot of advantages for a company like FB: HR can update info from everywhere (they might not be in the same office), you can immediately deny or block a card everywhere, you have an audit log etc.. They're not having this for fun.
Akso, it's likely not on an fb subdomain, but something like office.security.fb-infra.com (example). It just happens to be that fb-infra.com is using the Facebook DNS server.