Vera Menchik Jewish?!

Source: See Below

Moshe Roytman, a frequent correspondent, sent me the following headline, from Unser Express (in Yiddish), Sept. 20th, 1929, p. 15, about 'The Jewish Maiden Vera Menchik, which had Defeated the Greatest Chess-Players in the World'. 

What evidence is there that Menchik was Jewish? Technically it is possible that her father was since Menchik is indeed sometimes a Jewish name: a diminution of "Mann", i.e., "little man", as Jewish Family Names and Their Origins (Guggenheimer & Guggenheimer, Ktav Press 1992, p. 507) notes. But that hardly means all those with that name are Jewish -- any more than all those named, say, Rosenberg are Jewish (Alfred Rosenberg, to name one, was one of the major Nazi war criminals tried in Nuremberg, for example). 

Also, it is possible (technically) that her mother, Olga Illingworth was Jewish -- Illingworth is certainly a British name, from her father, but her personal name is Russian, so it is possible her mother was Jewish despite her father's name. But this seems unlikely as her (Olga's mother) first name was Mary Illingworth.

The most likely explanation seems to be that Unser Express was, simply, misled by Menchik's last name into assuming that she is Jewish, but is it possible that she was in fact Jewish, or "half Jewish" (i.e., on her father's side, which would not make her Jewish by Jewish law)?