Do they expect a company to believe them when they say "Yes, that anonymous social profile is actually me, John Emu maker. Really." Then if they proove it, by logging in and posting a known sentinel for example, do they expect everyone on that interview loop to keep their secret?
Companies generally don't take anonymous credentials.
This is a little too risky since it could wind up with someone revealing their identity inadvertently or otherwise. If you truly want to be anonymous you should not be leaving so many breadcrumbs. All it takes is for a former employer to have a security breach and someone to point out that they found your real identity.
Companies generally don't take anonymous credentials.