Of course. Private ownership itself is just explanation of the historical context, not proof that the right existed.
Having read Heller, the various drafts of the Bill of Rights, and some of the correspondence, I don't think anyone that has done the same can make an honest originalist argument against the private right.
In particular, I think the linguistic argument about militias relies on a neologistic definition that is particularly misleading.
People can make valid living constitution arguments against the second amendment all day and all night, but these seem particularly out of favor. I think this, more than anything else explains the Heller decision in 2008
