The Stanford Cardinal would have to win out for this scenario to be on the table. But if Stanford won out (which would include a victory over Oregon next Saturday night) and ended up in the BCS title game, then the Pac-12 spot for the Rose Bowl would open up.
As we all know, the Rose Bowl would love to set up the traditional matchup between the Big 10 and the Pac-12. Last year though, a new provision in the BCS required the Rose Bowl to take the top non-automatic qualifier if they fit BCS parameters, which the undefeated TCU Horned Frogs ended up doing. Since this provision only existed for one year, that means the Rose Bowl will likely choose the Pac-12 runnerup in the BCS rankings.
The Oregon Ducks would be clearcut second place finishers if they dropped games only to LSU and Stanford and would probably still make the top 14 BCS cutoff. That probably wouldn't happen if Oregon got upset by Washington. I explain over at Pacific Takes the parameters by which UW could find their way to Pasadena.
Currently UW is floating outside the top 25, but Washington upsetting Oregon and USC in subsequent weeks and then winning out against Oregon State and Washington State might just be enough to push them into the top 14, ahead of Arizona State (presuming they don't win out and finish with at most three losses).
Oregon-Stanford might be for top dog Pac-12 status next Saturday night, but Oregon-Washington could be where the fate for the Rose Bowl is decided.