People are predictable, a lot of the time. This is why we can't dismiss any resource, completely.
I started looking into it when I saw the clip of Patsy Ramsey saying "we loved that child".
I remember the first time I saw that, the hair stood up on the back of my neck and I had no idea why, as I didn't actually know too much about the case. I started looking into why I got the gut feeling I did when I head her say that.
Statement analysis is like the study of body language...one gesture or phrase on its own means nothing, but measure it all together and it cannot be disregarded entirely, as it is essentially the analysis of human communication. It is statistically based, therefore rooted in cold hard numbers.
Some of the premises I agree are far fetched, and I would disregard. Others, though, like the distancing language PR used, is the sort of thing that experienced LE most definitely take note of. You will often hear that investigators get a "gut" feeling or something didn't "feel right"...they are subconsciously picking up on a word, an unnatural response, an unusual effect, which leads them to a suspect.
As for profiling (SA is part of this greater science) one profiler even said that the suspect would work in/for/near law enforcement, drive a certain vehicle, be a certain age, and speak with a STUTTER...even though there were no witnesses.
How on earth?
But it was correct...BTK, IIRC. He was right under their noses the entire time. The profile was so precise it was largely disregarded at the time.