Mr. Herbert Halsegger had notified us that he had found the "Ganef" story - from the "older British player"'s point of view. In the Weiner Shach-Zeitung of Jan. 1933, pp. 18-19, in an interview with Viktor Teitz, Teitz reminisces about Burn, Blackburne, and others. In this version, Blackburn speaks of a "younger player" who exclaimed that "the old Ganef managed to swindle me after all!" and Blackburne finally asks the crucial question, whether a Ganef is a gentlemen or not.
One problem with the claim that this is Blackburne is, as Mr. Halsegger notes, only played with Nimzowitsch twice, and beaten him once (St. Petersburg, 1914). Calling that game a "swindle" - if, indeed, that is the game - is somewhat of an exaggeration. Computer analysis says Nimzowitsch had an advantage at one point, but was certainly not clearly winning. Another problem is that the story, oddly, comes in several versions, but seems to often only mention one of the players, never both.
Added 29/10/21: Mr. Halsegger notes Edward Winter had investigated the issue, as can be seen in Chess Notes #6513. that the story has several versions, and sometimes mentions both the (alleged) players - always Blackburne, but with various opponents and observers.