As I mentioned in the previous thread on this topic:
The dismissed cases linked to in the OP are even further down the scale, IMHO–in that you simply have people who falsely claimed to have been a veteran, or to falsely claimed to have served in a particular conflict, or to have falsely received a medal, or some combination thereof.
I can see that making a false claim for something that occurred in the past might indeed be protected speech, for all the reasons that have been discussed.
I would have more of problem with someone falsely claiming to be an active-duty servicemember, and would take the most issue with someone actually putting on the uniform of an active-duty servicemember and impersonating a servicemember–like the fake Marine discussed in the earlier thread. In my mind, these actions are little different from someone falsely claiming to be a police officer, or more seriously, actually putting on a police uniform and impersonating a police officer.
As one of the articles linked to in the OP states: