Anybody who sings through their nose like that hasn't had proper voice training. I bet Hetty could tell us more about that.
I missed both of last week's episodes ... was really on bedrest last week and sitting up in front of the TV just wasn't an option. :( (But we bought a recliner yesterday so I hope to be back in the swing this week!)
As for why people sing "through their noses" -- well, ideally you would like a *blend* of resonances. Your whole head (but especially your nasal passages) are one echo chamber, your mouth and throat are another echo chamber, and your chest is another. (Really, your whole torso, head and neck have some resonance value.) As you sing in different ranges (head voice or chest voice, high or low) the emphasis passes from one chamber to another. People who sing through their noses usually have had no training, or it's possible they've had some bad training. You can learn to "place" the resonances in different spots (for instance, singing in chest voice, you still might want a fair amount of nasal placement to give your voice a sharper edge so you don't sound too "hooty"), and sometimes bad teachers who don't really know what they're doing can cause young singers to get kind of screwed up that way. Also there can be physical issues ... for instance, someone with bad nasal allergies or infections might have trouble getting enough nasal resonance.
So much for my dissertation! LOL! Can't really comment on the singer in particular since I didn't hear them, though.