@indigomoth - It sounds like there are ways of overcoming the Reid technique, like the article says. Getting confrontational can work, although I think I'd be nervous to do that with the police, or with foreign captors for that matter.
Personally I don't think it should be used at all.
If it has got people to give false confessions in the past, it sounds like it has very little credibility. How could you ever really believe a confession that had been got with this technique?
On the other hand, I once saw an episode of a detective TV show (I forget which one) in which they had a suspect and were trying to get him to tell them where he had hidden the boy he kidnapped before the kid died.
In the end one of the cops kind of used that final step, pretending to sympathize with the criminal's motives in order to get him to confess where his hiding place was.
So it's hard to really put a firm rule onto when the technique should be be used and when it shouldn't I guess.