Air Wisconsin tried and failed to replace ALPA and they agreed to a joint contract which included the award. There are selectable sentences which might fuel your view, but in total I would not say with any certainty that the 7th Circuit pertains - bits and pieces maybe. Many Unions have been de-certified and replaced because of majority discontent. One of the NMB's missions is to conduct and provide oversight in representative elections. You can take from the 7th ruling what you will but one thing I perceived was the Judge sounded perturbed because Air Wisconsin had failed more than once in representative elections, not to mention the majority ratified an agreement which included the contested award."binding" arbitration is used everyday in civil cases and is most surely binding on the parties, it is federal law. The difference here is that this has never happened before and so the courts don't want to touch it. The 9th says they won't get into the "thorny" issue, because in fact the east has made it so, on one hand the union and company can amend a contract whenever they want, as they should. Of course never in the history of labor has a union been created to hurt a minority, btw the 7th circuit (air wisconsin case)said if that were to happen it would be illegal, all the 9th said is it hasn't happen yet so they won't answer the question.
http://ftp.resource.org/courts.gov/c/F2/909/909.F2d.213.89-3350.html