George Gershwin's "Liza"

I'm still making my way through the Gershwin albums.  This morning I listened to the seventh disc of the ten-disc set.  This one is subtitled The Later Broadway Musicals.

In "Liza" (performed here by Leo Reisman and His Orchestra), I noticed the line "we should make a date with Parson Brown."  It reminded me of the lines in "Winter Wonderland":

In the meadow we can build a snowman
And pretend that he is Parson Brown
He'll say, "Are you married?"  We'll say, "No man.
But you can do the job while you're in town."

I had to look up the dates though because I wasn't sure of the chronology.  "Liza" is from 1929, and "Winter Wonderland" is from 1934.  So either the writers of "Winter Wonderland" (Felix Bernard and Richard B. Smith) took an idea from "Liza," or the writers of both songs choose "Brown" for the surname of their parson.