Brainstorm:
A major site storing authentication data should store it in a separate physical server, isolate that machine so that administrative access is not possible from the net (NO path from the net through to ssh or console server access to the auth server should be possible... that includes internet -> internal employee machine -> auth storage server). NAT and firewalls are irrelevant, because they do not protect against incoming attacks through tunnels initiated inside.
That may mean physical console only login access, if the general internal network has internet access. That's a necessary usability trade-off something as serious as an authentication database for ten million paying customers.
The authentication protocol to talk to the auth server should only allow simple (easily parsed) requests; they should be rate-limited, there should be no provision to check multiple hashes at a time, and it should be impossible to export hashes out of the auth server without administrative (console) access.
Similarly prudent precautions can be taken for backups of the auth data. The backup server encrypts the auth database, before writing it to an attached disk or whatever the scheme is. Several high-level employees then have usb keys with asymmetric keys, any of which (or any n of which) will decrypt the backups.
You can't air gap the auth server, but you can limit the attack surface so dramatically that you have a high degree of assurance that it's secure against network attacks aimed at authentication data disclosure.
Someone can own the webservers and collect passwords and one time auth tokens, and can compromise 2-factor seeds for users who are just setting up 2-factor, but that's far more limited than gaining access to hashes or seeds from auth servers.