I understand that, as per the halakha, a Jew is absolutely obligated to save the life of a non-Jew, even if doing so requires of him that he desecrate Shabbat. (See, for example, this answer.) My question is specifically about the Mishna, Yoma 8:7.
The mishna in question reads as follows:
מי שנפלה עליו מפלת, ספק הוא שם ספק אינו שם, ספק חי ספק מת, ספק נכרי ספק ישראל - מפקחין עליו את הגל. מצאוהו חי - מפקחין עליו, ואם מת - יניחוהו
If a wall falls on somebody [on Shabbat] and it is uncertain whether or not he is there, whether he is alive or dead, or whether or not he is Jewish, we remove the rubble from him. If he is found to be alive, we continue removing it from him, but if he is dead we leave him.
Since the removal of rubble constitutes an activity that may be prohibited on Shabbat (perhaps the possibility of carrying four cubits in a public place), we don't do it if the only purpose it serves is to honour the dead. But in the event that it might enable us to save somebody's life (even if only for the briefest moment - Bartenura), we set aside Shabbat for the purpose of excavation.
It seems fairly obvious to me that the mishna's threefold formulation (there or not, alive or dead, Jew or gentile) is one in which the latter provisos would each render the search unnecessary if all doubt concerning them was removed. So, for example, if it is known for certain that the person is dead, we do not search through the rubble. If it is known for certain that the person is not there, we do not search through the rubble. If it is known for certain that the person is not Jewish, is not the implication likewise that we do not search through the rubble?
[Note: I reiterate that I am not asking a question about the halakha. The halakha mandates of us that we save a non-Jew's life on Shabbat. I am asking only about the correct historical interpretation of this mishna.]