The BYU football team made it clear that it would turn down an opportunity to play in the 1977 Fiesta Bowl — then held on Christmas Day — if it were to win the Western Athletic Conference championship, because that year Christmas fell on a Sunday. The Cougars ended up winning the WAC title that year to earn a bid to the Fiesta Bowl, but instead traveled thousands of miles across the Pacific Ocean to play a pair of exhibition games in Japan.

BYU didn't turn down an invite to the Fiesta Bowl because they NEVER received one. They tied for first place with ASU that year, but lost to ASU in head to head match-up, 24-13, thus giving ASU the tie-breaker. ASU received the auto-bid invite as the WAC Champion from the get-go. 

Everyone back then was hoping that BYU would win the WAC outright and make a statement by turning down the Fiesta Bowl because it was on Sunday. But along the way, they could not get by ASU. 

I've been hearing this: "but instead traveled thousands of miles across the Pacific Ocean to play a pair of exhibition games in Japan" for years, but it just isn't true.