So in the direction LAX/BNE (as per the OP's case) what other airlines are you going to be connecting to besides QF or JQ? TT or VA would be booked on separate tickets so would not show up as oncarriage flights anyway. It would be quite easy to rebook someone LAX/BNE then on to PER, DRW or CNS 24 hours later if they were bumped to the next day so I don't think having a connecting flight is necessarily a 'get out of jail free' card.
Even if the downgrade was in the other direction ie BNE/LAX & the pax were on a non 081 ticket (eg Alaskan ticket with an 027 prefix) the particular flight coupon of the BNE/LAX sector still belongs to QF and AFAIK they have authority to reissue their coupon plus any coupons thereafter on that eticket eg if the remainder of the journey was BNE QF LAX AS YVR.
In any case if pax were bumped BNE/LAX/YVR the pax probably wouldn't even need to have their eticket reissued anyway unless there was a change of routing, so the original flight coupons could most likely be used BNE/LAX/YVR 24 hours later if required.