[walrus1066]

'I'm willing to bet that when a company wants to hire a two sigma candidate they don't go through all this nonsense'

Can testify to this, interviewed via referral, was still asked some algo-trivia, didn't do too well on that but still got a decent offer, mainly because referee vouched for me based on their experience working with me.

[strangerlands]

Either (a) they want you or (b) they want someone like you. If (a), they find any reason for hiring you, if (b) they find any reason for not hiring you. This explains most of the interview dynamics, especially at large companies.