Here is Boise St.'s football record by season:
2012: 11-2 MW Champs #18 AP Poll
2013: 8-5 Not rated
2014: 12-2 MW Champs #16 AP Poll NY 6 participant
2015: 9-4 Not rated
2016: 10-3 Not rated
2017: 11-3 MW Champs #22 AP Poll
2018: 10-3 #23 AP Poll
2019: 12-2 MW Champs #23 AP Poll
So, in the last 8 years, Boise St. has won 4 MW Championships and been ranked 4 times, never higher than #16. These are very good records, but they are not the accomplishments of the Boise St. from 2002 to 2011 when they were ranked in the top 10 four times and the top 16 eight times.
Boise St. plays in the MW which is not as strong as the AAC, so going to the AAC would probably mean additional losses, although if they won the AAC, it would probably mean a trip to a NY 6 bowl. Maybe going to the AAC would increase the media dollars and prestige of the AAC, but Boise St. has not built a huge fanbase that will be accepting of cyclical football performance.
And, no way Boise St. can join the AAC for all sports as the travel costs would be too high.
I think Boise St. and the MW will figure out a way to make peace as it is in both parties interests.