If you claim doc: 50/50 doc dies. If doc dies, you kill vig and win instantly. 50/50 you die, which wouldn't change anything.
If you claim blue: 50/50 blue dies. If blue dies, vig kills you 'cuz doc covers vig. if you kill doc, vig kills you, if you kill vig, doc saves vig. You lose. if you die instead of blue, no outcome
That's why you claim doc instead of blue in final 4.