In "A Late Quartet", is the Pablo Casals anecdote based on a true story?

From the autobiography of Gregor Piatigorsky, "Cellist":

"Mr. Casals." I was introduced to a little bald man with a pipe. He said that he was pleased to meet young musicians such as Serkin and me. Rudolf Serkin, who stood stiffly next to me, seemed like myself, to be fighting his diffidence. Rudi had played before my arrival, and Casals now wanted to hear us together. Beethoven's D-Major Sonata was on the piano. "Why don't you play it?" asked Casals. Both nervous and barely knowing each other, we gave a poor performance that terminated somewhere in the middle.

"Bravo! Bravo! Wonderful!" Casals applauded. Francesco brought the Schumann Cello Concerto, which Casals wanted to hear. I never played worse. Casals asked for Bach. Exasperated, I obliged with a performance matching the Beethoven and Schumann.

"Splendid! Magnifique!" said Casals, embracing me.

Bewildered, I left the house. I knew how badly I had played, but why did he, the master, have to praise and embrace me? This apparent insincerity pained me more than anything else.

The greater was my shame and delight when, a few years later, I met Casals in Paris. We had dinner together and played duets for two cellos, and I played for him until late at night. Spurred by his great warmth, and happy, I confessed what I had thought of his praising me in Berlin. He reacted with sudden anger. He rushed to the cello, "Listen!" He played a phrase from the Beethoven sonata. "Didn't you play this fingering? Ah, you did! It was novel to me...it was good... and here, didn't you attack that passage with up-bow, like this?" he demonstrated. He went through Schumann and Bach, always emphasizing all he like that I had done. "And for the rest," he said passionately, "leave it to the ignorant and stupid who judge by counting only the faults. I can be grateful, and so must you be, for even one note, one wonderful phrase," I left with the feeling of having been with a great artist and a friend.