The union is referring to statements made by various politicians, such as those in the state Legislature threatening future tax subsidies for Volkswagen if the plant voted to unionize, and especially US Senator Bob Corker's late bombshell that he had been "assured" by an unnamed source that the plant would get a new crossover to build as long as it rejected the union. Some outside observers at the time said that could be enough to invalidate the vote before it had been completed.
Some questionable statements have come from the pro-union side, too. The UAW had its own dustup over its tactics in September 2013, when eight workers at the plant filed complaints with the NLRB accusing the UAW of trickery. And in January of this year Reuters reported that Bernd Osterloh, the German workers' representative on the VW Board, said, "Chattanooga would make sense from an economic viewpoint if the company could offset the higher personnel costs compared with Puebla." There's little chance that would happen if union representation were approved. Just a month later, after the vote and because of the rumbles that proceeded it, Osterloh said another plant "does not necessarily have to be assigned to the South again." All throughout the process, the actual Tennessee workers have been the quietest party at the dance.
The UAW has seven days to give evidence supporting its appeal to the NLRB. The latest observers in the Reuters piece, though, think that the UAW will have a hard time winning, because "labor law does not limit what can be said in a union election campaign by politicians, as long as they are stating their own views and not doing the bidding of management."