Although the basic shape of the story is correct, recently published biographies differ in the particulars. Beethoven by Barry Cooper (NY: Oxford University Press, 2000) and Beethoven: The Music and the Life by Lewis Lockwood (NY: Norton, 2003) both state that Ignaz Dembscher was an amateur musician who organized chamber music sessions at his home in Vienna. He wanted to play the String Quartet in B-Flat Major, opus 30, at one of these gatherings, but he had not attended the concert premiere of the work in March 1825. When Beethoven’s secretary Karl Holz relayed the request, the composer said Dembscher would have to pay the fifty-florin subscription price he would have been charged at the concert. Holz reported that Dembscher’s joking response had been “Muss es sein?”
So perhaps Beethoven never had a verbal exchange with Dembscher face-to-face, but the latter’s question caught the composer’s fancy, and sparked him to compose the joking canon (“It must be, yes, take out your wallet!”), and a year later, the more portentous quartet.