There was an approximately 73 page document outlining the selection criteria for the Olympic Team that was published before the 2013-2014 season ever started. It very clearly outlined the fact that Championships is not (nor really has it ever been) an Olympic Trials event. In other words, even though it usually is the medalists at Championships that are selected, it does not have to be.
The selection criteria included (among other things) a number of competitions held over the past year. These included 2013 World Championships, the 2013-2014 Grand Prix Circuit and Grand Prix Final, 2013 Four Continents Championships, 2013 Championships placement, 2013-2014 Junior Grand Prix Circuit and Junior Grand Prix Final, and other international competitions.
Based on the stated criteria that was published, I believe the International Selection Committee actually made the right choice. If anyone was to be left off, it should have been Mirai. Don't get me wrong, I was happy for her to land her jumps at Championships. However, based on the criteria she was not as strong of a choice as either Polina or Ashley.
Polina got the nod based on her placement at Championships this year and last year, as well as winning both of her JGP events and placing 4th in the JGP Final. Plus, let's be realistic. She has one of (if not the) most technically loaded programs of any of the U.S. ladies. Her PCS needs to improve, but that's typical of a just rising junior. Plus, she has the look and jumps of all of the little Russian jumping beans (like Lipnitskaia) that they will meet at the Olympics.
Ashley, although not great under pressure, has a decent technical difficulty in her program. She has the PCS to match it when she skates well. In addition, her placements in the Grand Prix, Grand Prix Final, and Worlds all went to her credit.
Mirai, though, has not had a good career since the Olympics in 2010. Yes, she has international experience. However, in the past year to two years, she has done poorly at Championships, she has done poorly at her Grand Prix events, and (if I remember correctly) she did not qualify for any event where the international team was selected based on results of another competition (Worlds, Four Continents, etc.). Although her jumps were technically sound at Championships, her program was empty. There were pauses between elements where she really wasn't doing anything, or just visibly breathing.
Was there some politics and publicity involved in the decision? Sure. There always is, no matter what sport. Do I feel bad for Mirai that she finally skated two clean programs at Championships and didn't get the team? Yes. But did she deserve based on the stated criteria for selecting the team? Probably not.