It would have made a HUGE difference.
Had her parents not been naturalized before she was born, she then would have only been a native of the soil owing allegiance to a foreign nation; however her parents were naturalized and had sworn an oath of total allegiance to the United States and thus she was born owing no allegiance to any foreign nation as stated in the 1866 Act.
She would not have been natural born, true. But she still would have been 14th amendment citizen, as the examples in given in the opinion make clear, some of which involved birth to alien parents, in the US, and in which the person was declared to be a citizen.