So if @USM Professor paid $3,000 each and $5,833 was the gift portion then the gift portion would be used as the basis because it's greater than the amount paid.
I think you misread 1(ii). The basis is whichever is greater...the amount paid ($3000) or the giver's basis ($8,833). The giver (sibling) received a stepped up basis, and that basis is what is transferred. Don't be confused by rule (2), that covers increases to basis if the gift has increased in value more than the giver's adjusted basis.
Example: Suppose my friend owns property that he bought for $10,000 that is now worth $20 million. He gives me the property. He is required to pay gift tax on about $7 million (because the $20 million gift is more than the lifetime exemption of $13 million). My new adjusted basis in the property is $7,010,000.
That doesn't apply here because the property did not increase in value between the father's death and the sibling's gift.
