Question

Another point from the meal at Rabbi Avigdor Nebenzahl’s on Simchat Torah.
Someone arrived and said that he had heard at some conference on medicine and Jewish law from a certain professor that Rabbi Shlomo Zalman Auerbach told him about Rabbi Yishmael the High Priest, who took the severed head of his fellow and cried, “Alas for the tongue,” etc. …
But he was the High Priest, so how did he become impure through contact with a dead body?
And he answered: apparently the Romans had some kind of custom of granting a last request or something like that… and when they saw that Rabbi Yishmael was dealing with the head, etc., they let him continue until he finished. And saving a life, even only temporary life, overrides the prohibition for a kohen to contract impurity from a corpse.
And from this we learn how much effort must be made to save the sick, even for only temporary life, etc.
Rabbi Avigdor Nebenzahl said that in his opinion this took place inside a house, and once the dead person died, everyone present there became impure through tent-impurity, and there is no prohibition against adding impurity, so there is no problem in taking the head. [Rabbi Yishmael was forced to remain in the house where the Romans were killing people.] On the contrary, this even gives greater cause for an appropriate eulogy.
 
Who is right, the rabbi or his student?
   Or both?