If BYU was going to wage PR war with UW/the PAC 12, it would have been smart indeed to publicly accept the game and make them look foolish for backing out.
But this was never supposed to be a PR war. There is a reason you hear about scheduling from BYU sources only in the form of official announcements with dates and times. These negotiations are supposed to be confidential. They are never supposed to rise to the level of a PR war. Otherwise, you may scare potential callers from even picking up the phone.
It is unfortunate that this leak happened, and very much unbecoming of the party that allowed it to leak. That's not how business partners should be treating one another.
Hopefully in the long run the message other universities hear from this fiasco is that BYU can be trusted to do right by them.