no. not at all
first, there is nothing which requires the employer, in this instance, northwestern, to do anything other than negotiate with the new bargaining unit in good faith
if the employer's position is it is without the funds to pay anything more then it would be foolish to agree to pay that which it does not have
however, if it makes such an allegation and the parties are at impasse, it will then be a matter elevated to a court or more likely, arbitrator, for a final resolution. that objective third party will review all of the facts. and if the arbitrator found that the employer was less than truthful about its financial ability to pay then it will make a award in the union's favor. if it finds that the employer does not have the money to offer additional compensation, that objective third party will make a decision in the employer's favor
but now i ask you, if the university is found to be paying its coaches annual salaries in the millions of dollars, how legitimate is the employer's argument that it cannot afford to pay the players