A Giant Barely Out of his Teens - and Stravinsky??

I cannot recall my having related the following story to you. I don't believe that I have, and it is really a rather piquant little tale:
Barely twenty, George Gershwin became one of the most famous and sought-after composers of his time just months after the legendary Al Jolson sang the young man's song, one of the most popular tunes of that day, "Swanee."
Gershwin became, almost overnight, the toast of New York, and his fame spread quickly even to as far a place as Mother Russia.
Gershwin was bedazzled by all of this recognition and attention, and soon thought, probably with some embarrassment, that he ought to accumulate more knowledge about music by taking lessons in music language and theory. The great Igor Stravinsky, one of the twentieth century's true musical giants, happened to be in New York City at this time, and so Gershwin sought him out.
He was ushered into Stravinsky's office or den (I know not which). Stravinsky, who was generally known to have the social grace and disposition of a Puff Adder, without looking up, asked the young genius, "why are you here?" To which Gershwin replied that he would like to take some lessons with him.
After a short pause, strange words emanated from Stravinsky; namely, " what is the size of your bankroll?" Stunned, Gershwin managed - "Sir?" Stravinsky then looked up at him, and asked "how much do you have in the bank?"
Staggered, Gershwin, who really had no specific idea what monies he had accumulated, gave, rather haltingly, an amount, to which Stravinsky then resumed looking down at whatever was on his desk, and muttered, "It is I who should be taking lessons from you."
That ended the conversation.
Now, I relate this tale to you, without being absolutely positive about its being a reality - I have already cited examples in previous blogs about, in certain instances, even Primary Source material being suspect; however, I am telling you this tale because Ira Gershwin, George's brother, related that he heard George himself telling this experience more than once at the many parties the Gershwins held in New York and/or Hollywood with countless celebrities present as guests, both from Hollywood and New York.
Believe it or not, one of the guests at one of these Gershwin parties was none other than the titan Arnold Schoenberg - yes, he was there - I have a copy of that film on one of my DVD videos.