The Militia Act of 1792 concerned the authority of the President to call out the Militia of each State “whenever the United States shall be invaded, or be in imminent danger of invasion from any foreign nation or Indian tribe…”
Oh, it is much more significant than that,
R-S. You are referring to the wrong provision of the Act(s), my friend. What the Militia Act is based upon is Congress' authority, not that of the President. Indeed, Congress is required
To provide for organizing, arming, and disciplining, the militia, and for governing such part of them as may be employed in the service of the United States, reserving to the states respectively, the appointment of the officers, and the authority of training the militia according to the discipline prescribed by Congress
It says so at the beginning of the Act that I quoted. What has caused the confusion, I think, is that there are two portions of the Acts - one concerning the president's authority, the second, the section I quoted, addressing the organization of the militia.
I think that you have also conflated two purposes of the arming requirement. The first is to enroll all able-bodied men, the second is to address their equipage. Note, by the way, that only personal arms are addressed there, as
armaments, weapons not personally carried/supplied by the individual, remain the responsibility of the government, State or Federal, to supply.