Facebook Employees can login as you without your credentials
facebook.com
facebook.com
But... if you are going to build a service used by the public, you really have to face the fact that these ARE the people you wanted to be useful to in the first place. And with that, you had better be able to log in as them without asking anything more than just their name. Anything else is simply far too high of a cognitive load to place on them.
I can't remember if I'm thinking of FB or another service, but I seem to recall there even being multiple levels of impersonation, so employees masquerading as users for debugging purposes have to explicitly request write access or messages access, but I'm not 100% on that.