NL Tourney Rule Check

[Precept2]

I played in a tournament yesterday when the big blind of a hand got knocked out.

The person who was going to be big blind said:
The Big Blind skips him and he becomes the small blind, while the person on his left becomes the Big blind.

I said:
There is no small blind, he's still the big blind (it doesn't skip him), and the person dealing was going to deal two hands in a row, while he would be the small blind on the next hand.

He said:
That's not how they play it at PartyPoker.

I responded:
That's how they play it at PokerRoom and at the Trop (in AC).

Who's right? What's the ruling?