Morality is irrelevant, although it's true everyone moralizes and assigns value. We can't help but view the world through value-loaded terms. The question seems to be, "Which morality?" for there are different moralities besides Jewish-Christian-Islam-liberal-democratic-humanist-socialist-etc morality, I've also heard some called "Slave-morality," and for a good reason, for it turns people into mindless robots; autonomous and moral now being two mutually exclusive terms.
Moral nihilism doesn't argue that morality doesn't exist, it simply states that nothing is intrinsically moral or unethical. Living things intrinsically have values. From plants to people. That's why moral nihilism might be "logically" true but its not "factually" true.
Many people in similar situations, often say the same things. "I didn't think about it." "I just acted, I don't know why." "I felt I had to." "I felt I was being swept along." Those reports sound like reports of subconscious drives to me. I am familiar with such drives, I have experienced them myself, so I think the reports are plausible, and indicate that humans have a vestige of biological value, which can overcome us in extreme conditions.
I can't think of any reason why I should value my life, except that I do. I just do. It is beyond reason. It is merely a part of my being.
I believe our actions countered reason in the rational sense, but some of the people who rushed around trying to save people in the fire disregard for their own safety and value for their own lives. Their counter-values (to their own lives) came from irrational sources, but they did not contradict reason. Not all reasons are reasonable in the rational sense. Most values have irrational roots.
So from the context of moral absolutism, what those people did jumping to their deaths was morally wrong; trying to save others, risking their lives, without slightly thinking about their wives and children at home? Of course I think moral absolutism is a bunch of bullshit.