it absolutely DOES matter. If the person doesn't have a mental disorder, then it doesn't matter whether they can't appreciate the severity of their condition or not. The whole point of decision-making capacity (and the reason why psychiatrists and psychologists are brought in to weigh on this question) is that we presume people have the ability to make decisions unless their is a reason to believe that their mental functions are impaired to the extent that they cannot. If you don't have a mental illness, neurocognitive disorder, or intellectual disability, then you still have decision making capacity
even if you are unable to check all the boxes of the Appelbaum and Grisso criteria. Put simply,
it is NOT enough to not communicate, understand, appreciate, and/or reason, but this deficit has to be due to a mental impairment. If the reason for the deficit is a cultural belief (i.e. an overvalued idea) then you have no justification for denying that patient their autonomy. decision-making capacity is fundamentally rooted in autonomy, because the whole point of evaluating capacity is to
promote autonomy. If you allow someone to make a decision that they would have not made if they did have capacity, then you are depriving them of their autonomy as the decision is being fueled by delirium/psychosis/dementia etc. On the other hand, if someone has a deep personal conviction that is fundamental to their identity (for example being a QAnon believer who thinks COVID is a hoax to take down Trump etc), then that pt's beliefs about their illness, and subsequent decisions, even if they fly in the face of medical reality, are tied to that patient's autonomy and you have no justification to deny them their right to make decisions you disagree with if they aren't deemed to be psychotic.
It is unfortunate how poorly taught capacity evaluations are that so many psychiatrists do not appreciate this basic point.
ETA:
From Scott Kim's Evaluation of Capacity to Consent to Treatment and Research. Oxford: OUP, 2010