Punch Brothers' "No Concern of Yours"

This morning I listened to Punch Brothers' Who's Feeling Young Now?  I'd forgotten that there was whistling near the end of "No Concern of Yours."  It doubles the melody during the "When your name is on his building" part (at least I think that's what the lyrics are).  The whistling itself took me a few listenings to discover, if I remember correctly.

But rediscovering it now, I realized that it's sort of related to the lyrics.  The actual concern in the song isn't really defined since the speaker/singer is trying to avoid talking about it, but his insistence to not talk about it suggests that it's important.  (At least, that's my understanding.)  And I think the whistling helps to indicate that.  It's the same sort of thing as in old movies and television shows where people start whistling to disguise the fact that they're nervous about something.