The manager didn't know what he was talking about.
A minimum wage, assuming it is higher than the prevailing wages would otherwise be, allows union wages to be higher than they would be if they had to compete with below-minimum-wage competition.
If non-union workers were cheaper, the incentives would be for management to either go with non-union workers, or lower the wages for union workers to be competitive.
The higher the minimum wage, the higher union wages can be, since lower wage competition becomes illegal. This is why unions always support higher minimum wages.