Yes. HACE symptoms should definitely be included along with AMS,
I was totally focused on AMS, not just for those around me but for me as well. I was doing word problems and things like that in my head.
The only odd thing about our companion was that he never complained about any AMS symptoms. His gait was my first indication that something was wrong. But it was very obvious at that point.
There was also the fact that he improved very quickly with rest. He was nearly normal by the time we left the summit since he gotten nearly 30 solid minutes of rest. But it took a very short time for the symptoms to return.
He must have had AMS prior to HACE and just kept quiet about it. The guy was a fireman and I think he had a bit of ego working against him. He was never able to keep up with us even right from the beginning so I have a feeling he was pushing way too hard and not wanting to voice any complaints.
At one point in the middle of us talking to him he said "Why is this kicking my ass so hard but not affecting you guys?" so he was really feeling excluded I guess.