The Shulchan Aruch (O.H. 618, based on Yoma 82a,83a) lists rules for when a sick person should eat and not eat on Yom Kippur, judging by his and his doctors' judgment of whether the sickness is life-threatening. If I correctly understood what was written*, then the following six rules emerge from the discussion.
Should you break the fast ("yes") or not ("no")?
1. Doctor says yes, patient says no -> yes
2. Doctors disagree (except when one says yes and more than one says no), patient indifferent -> yes
3. Doctor uncertain, patient says no -> yes
4. Doctors disagree, patient says no -> no
5. Doctor says no, patient says yes -> yes
6. Doctor says no, patient uncertain -> no
It is clear that rules 1-4 are intended to determine the medical reality as accurately as possible. We try to figure out the situation, and if we end up unsure, we generally break the fast to avoid any chance of killing the patient.
Rules 5 and 6 however seem to operate on a different premise. In these rules the doctors are sure that there is no danger, so based on a purely medical evaluation, there is no basis to break the fast. If so, why in rule 5 does the patient's opinion override the doctor's and dictate that we violate the fast?
I think reason is psychological. If the patient is convinced that his life is in danger, he will find it extremely distressing to not eat. He will think that we are killing him by telling him not to eat. If he was sick but not in real danger before, this distress might put him in real danger. Thus we feed him, on the presumption that psychological factors can affect medical outcomes.
Of course if a totally healthy person became unreasonably convinced that they were about to die unless fed food, the psychological impact of not feeding them could be ignored. But if they are already sick enough that doctors had to be consulted about the possibility of breaking their Yom Kippur, then the psychological effect might be very significant.
In rule 6, by contrast, the patient does not have an opinion on whether he should break the fast. So telling him to eat will not distress him, and there is no reason not to follow the doctors' opinion that he should keep fasting.
I find it interesting that this kind of psychological factor is included in the halachic decision making process for this situation. The medical ethics people should have a field day with this one.
* This is not guaranteed. I'm pretty exhausted right now - it's post-fast, and it wasn't an easy fast. And the buses I've written this on have been full of distractions - bad conversation and bad music.