The fault rather lies in the use of torture by interrogators, which is not Constitutional. However such interrogation tactics would not be allowed in US Military courts either.
The issue is much more broad than Constitutionality. The issue is whether as a nation we are willing to abide by international law and to abide by the law of "Natural Rights". The laws of "Natural Rights" were recognized and accepted in the United States Declaration of Independence which precedes the Constitution. Simply stated, all human beings have undeniable rights regardless of nationality or status.
Our mistake was to consider using such unlawful interrogation, and to proceed to break these laws as a government. Any one of us would readily admit that none of our Founding Fathers would have ever agreed that such torture was moral, right, or legal.
Those who believe in American "exceptional-ism" apparently believe that Americans are above the law while living in a Republic which is defined as a government of laws.