They authorized action, these vessels were previously legally armed.
Google search the papers for the privateer "Lucy" if you doubt me.
So yes, by law and by tradition US citizens may own ships of war.
Fascinating reading.
True, as long as you kept them in port or dry dock you could certainly own them.
But all armed merchant ships- not just warships- were so heavily regulated by the federal government because of how much trouble they could cause in foreign affairs that it doesn't seem the Second Amendment was considered to apply to them.
"...SEC. 3. And be it further enacted, That after notice of this act, at the several custom-houses, no armed merchant vessel of the United States shall receive a clearance or permit, or shall be suffered to depart therefrom, unless the owner or owners, and the master or commander of such vessel for the intended voyage, shall give bond, to the use of the United States, in a sum equal to double the value of such vessel, with condition, that such vessel shall not make or commit any depredation, outrage, unlawful assault, or unprovoked violence upon the high seas, against the vessel of any nation in amity with the United States; and that the guns, arms and ammunition of such vessel shall be returned within the United States, or otherwise accounted for, and shall not be sold or disposed of in any foreign port or place; and that such owner or owners, and the commander and crew of such merchant vessel, shall, in all things, observe and perform such further instructions in the premises, as the President of the United States shall establish and order, for the better government of the armed merchant vessels of the United States.