Most non religious people do not like coercive interrogation. Religion is supposed to be about loving thy neighbor and taking care of the poor. Which means, you would think religious people would be against such shady tactics .It is not always the case because one thing most religions do not like is when a group or person threatens their religious freedom. Then they loose all sense of their religious morals and ethics. Not all but many.
Jesus said, "Love your neighbor as yourself." Such things as "coercive interrogation" don't follow that tenet whatsoever because most of us would not want interrogation to happen to us. Therefore, why would a Christian value include interrogating another human being, even though that questioning doesn't include torture? Christian values are about love and acceptance, not manipulation.
Christians believe in showing kindness and not harming any of God's creatures. They adamantly defend the right to life and are against abortion. A fast majority do not believe in using the death penalty against criminals, no matter how heinous their actions are. Any interrogation that would incur physical harm would not be in line with a Christian's moral values.
No, the values adhered to by Christians does not permit things like "coercive interrogation," because Christian values tend to embody more of a philosophy of kindness, helping each other and fellowship. Practices such as coercive interrogation directly conflict with these Christian values actually. Anyone who takes part in these types of practices and tries to hide behind their Christian values is confused about their religion's values.
I doubt that something that is used as an advanced interrogation tactic, has any place in the religion. The fundamentals of the religion point towards this not being a possibility. The religion has it flaws,but its not in the their means to trick people into anything, people will believe anything on their own.