The MSM produces spin meant to pressure and drive behavior. The White House has very tight control on the press as evidenced by the documented coordination.
While your clarification is very helpful I think there is just such a spin effort being driven by the White House & party elite, meant to force the troops into line. The ramifications of using lies, obscuration & spin is that no one knows what is true and there is a loss of trust in GV’t. The uncertain and contradictory info also paralyzes Americans which benefits the Globalists.
The people being misled by the article are either 1) civilians who have never served, and therefore don't know about discharges at all, or 2) veterans who didn't read the initial article very closely, or at all.
The real issue is that even administrative discharges can impact your right to VA benefits, etc.. If I were to guess, troops who have not yet completed their first term of enlistment and refuse the vaccine would get some sort of admin discharge. Service members who have completed an initial terms of service would get an honorable because the blowback would be too much otherwise.
DD's just aren't an issue.