BYU, as the WAC champion, had a contractual tie to the Holiday Bowl.  Oklahoma, as the Big 8 champion, was contractually obligated to the Orange Bowl.  UW had lost a game, to USC, and as a result finished second in the PAC10, sending USC to the Rose Bowl.  Washington, without the tie to the Rose Bowl was basically a free-agent.  In the 80's most conference champions had a tie to a specific bowl, but almost all other teams then negotiated with bowls for a spot.  There less than 20 bowls at the time, so basically you either had to be a conference champ, or a Top 20 team to get a spot, unless you were one of the top teams in a big conference.

The Holiday Bowl had one of the lower bowl payouts at the time (~$500K if I remember correctly), and Washington decided that they would take a bigger payday, and a New Year's Bowl by going to play Oklahoma in the Orange Bowl, which they lost.

So, any sour grapes that UW had over the national championship that year are fully their own fault.  Under the system that was in place with voting at the time, an undefeated BYU won.  Washington could have chosen to play BYU in the Holiday Bowl and win it on the field, but chose the money and the chance to play Oklahoma instead.  They rolled the dice, assuming that a 1-loss PAC10 team that had beaten Oklahoma in the Orange Bowl would leapfrog an undefeated BYU, and they lost.