Maybe sibilance is what I am hearing and I'm just doing a poor job of describing it. It's kind of this "un-naturesness." Do you have any songs with very clear and obvious examples of sibilance that I can compare to?
One of the tracks you originally referred to "Closer To Fine by Indigo Girls" has many many clear and obvious examples of sibilance.
Sibilance - e.g. when a word with the letter S is sung there can be this prolonged ssssssssssssss sound. It can be quite sharp/bright/piercing to the ear.
Here is a YouTube video covering the topic: