Seeing Other People's Steam Accounts: The Christmas Caching Catastrophe

On Christmas Day, someone at Steam changed a setting and brought down their whole games platform. I wasn't expecting to do a video this Christmas, but when enough people tweet me, it turns out I can be convinced...
(I should note: while Steam have officially confirmed "a caching problem", I've got no privileged information about the specifics. It's possible (but unlikely, I think) this was a misconfiguration at Akamai, or a bizarre server bug that happened to exactly match a much more likely caching misconfiguration error!)