I appreciate what you are saying. In reality, changing only one condition will likely cause only a left or a right shift. Where the confusion comes in is when more than one condition is changing at the same time.
The problem with asking a question like "what happens at high altitude" is that many things change over a period of time. Are people asking about the immediate effects of the change in pO2, or to the response of the body after some period of time?
When I talk about examining the environment in which the hemoglobin is in, I am trying to show that something like 'high altitude' can have complex effects and a generic answer may not be possible.
I think the problem with these "high altitude" threads is not that people don't understand the physiology, but that the questions are not specific enough.
EDIT: I should also mention, though, that it definitely is possible to have a left shift at the lungs and a right shift at the tissues at the same time. In fact, that is the way it is supposed to work. The differing conditions of the lungs and the tissues is what causes the left and right shift (which can also be looked at as increased or decreased affinity for oxygen). If this were not the case, all the hemoglobin in the body would have the same affinity for oxygen, which would decrease oxygen transport.