As I understand it, the dispute is over the meaning of 'militia'. At the time, the 'militia' was considered to be any able-bodied male under the age of 40, and under the law's current definition of the militia, any able-bodied person between 17 and 40 is considered to informally be part of the militia (as opposed to the national guard, who are formally part of it)[1]. The question is whether 'militia' means just the national guard or includes the 'irregulars' who would've been expected to fight despite not formally being part of the military.

[1] https://www.law.cornell.edu/uscode/text/10/246