In the medical profession, physicians in training learn very early on that there is a subset of patients that are unlikely to survive despite any aggressive or invasive therapy, without which they would surely die.
The overarching commitment to helping people in life-threatening circumstances, however, demands that aggressive or invasive remedies be administered in the hope that the patient's life *could* be saved, even if the likelihood of improving the patient's condition by employing them is limited or unlikely. (In the interest of avoiding totally unnecessary suffering, however, doctors are not obligated to perform procedures that they know are absolutely useless, or futile.)
And, beyond the above, doctors who are sincerely committed to ethical and humane care are taught to rationalize aggressive or invasive measures of support of a patient even *if* they feel that particular patient has a limited likelihood of responding to them, because they know that perfecting a technique that may not help one patient today may go a long way toward helping another in the future.
I hope my metaphor is clear. I think all of the above is at work in the DT's mind by their commitment to Casey's apparently hopeless defense.