Our sunni fellows think that Abu Bakar become first calip because he led the prayer during the lifetime of the Prophet(pbuh) (even this is not proven nor Abu bakar mention about him for the Caliphate).
This narration of Bukhari testifies that Abu Bakar and Umar used to pray behind Salem (slave of Abu Hudaifa), if we believe in Sunni logic Salem shld be the Caliph of Abu Bakar and Umar then.
By the way according to our sunni fellows there is no big deal if anybody led the prayers, a cruel and sharia law breaker can be the leader of prayer.