blind structure at party

[vonteego3 0]

I'm sure I'm not the only one to come across this, but I don't recall ever seeing it discussed here.6-handed in a shootout, the BB gets knocked out. Next hand, there is no SB, and the BB is the following player... obviously, correct. On the following hand, the button suddenly moves to the player that was BB last hand, skipping his SB and the player following's BB... a pretty big deal when they both have <2000 chips remaining and blinds at 300/600.I'm not wrong in thinking the button should stay on the same player and have the BB become the SB and UTG be the BB the following hand, right?