Triage

In Igros Moshe (Choshen Mishpat 2, siman 73, part 2) Rav Moshe Feinstein ZT"L speaks of prioritizing two critically ill patients with differing prognoses, one who will only live a "chayai sha'a" (temporary relief) even with medical intervention and one who is projected to live a "chayai olam" (normal healthy life) with it. He says that were they to arrive simultaneously under your care, then one would be permitted (and in fact required?) to treat the patient who's has a better chance at survival rather than work with the patient who's prognosis is for "chayai sha'a" at best. However, if the "chayai sha'a" patient would come under your care first and you would begin his treatment it would be totally prohibited to leave him and treat the patient with the more promising prognosis. It seems to me that Rav Feinstein gives two reasons for this prohibition: The second reason given is because leaving his care would indicate to this ill patient that he has a worse or no chance of survival. This psychological fact and it's effect on the patients mental health would contribute to hastening his death and is threfore prohibited.
My question is regarding the first reason given. R' Feinstein seems to assume as a very basic and fundamental idea that being there first entitles this ill person to the continuation of his care. He says that in effect this "chayai sha'a" person has already acquired his place and as such cannot be removed from it even to save this more promising outcome. I do not see a source for this assumption anywhere. I have also seen this very same logic quoted from R' Shlomo Zalman Aurbach in the footnotes of the Nishmat Avraham (Y"D p.156) . What is the source for this halacha? Shouldn't the logic which dictates the p'sak when they arrive simultaneously, namely that with a chance to save one life choose the more promising outcome) still apply here?
Please post any suggestions.

Judah Goldschmiedt