I checked the holocaust site and found no mention of purple (or any mention of cross) cross attached to the symbol that jws wore.
I could imagine that some non-jw tour guide might have had a slight of the tongue. Aren't all the patches worn by concentration prisoners triangles or combinations of triangles?
What did each of the identifying badges mean?
The Nazis used triangular badges or patches to identify prisoners in the concentration camps. Different colored patches represented different groups. The colors and their meanings were:
A chart of prisoner markings.
— KZ Gedenkstaette Dachau
The "Asocial" category was, perhaps, the most diverse, including prostitutes, vagrants, murderers, thieves, lesbians, and those who violated laws prohibiting sexual intercourse between Aryans and Jews. In addition, while the brown triangle was used for gypsies under certain circumstances, they were more often forced to wear the black triangle categorizing them as "asocials."
Some patches included letters on the triangles to further distinguish among the various groups in the camps. Most commonly, the letter indicated nationality, e.g., "F" for franzosisch (French), "P" for polnisch (Polish), "T" for tschechisch (Czech), etc., but it could also denote special sub-categories of prisoners. For example, the white letter "A" on a black triangle signified a labor disciplinary prisoner (Arbeitserziehungshaftling), while a black "S" on a green triangle identified a strafthaft, or penal prisoner. In addition, the word Blod on a black triangle marked mentally impaired inmates, and a red and white target symbol set apart those who had tried to escape.
For Jewish offenders, triangles of two different colors were combined to create a six-pointed star, one triangle yellow to denote a Jew, the second triangle another color to denote the added offense. For example, a Jewish criminal would wear a yellow triangle overlaid by a green one; Jewish homosexuals wore pink triangles over yellow.
Outside the camps, the occupying Nazi forces ordered Jews to wear patches or armbands marked with the star of David, though the specific characteristics of the badge (size, shape, color) varied by region. For example, some yellow stars were marked with a large "J" in the center, while elsewhere the patches had "Jude" (or "Jood," "Juif," etc.) stitched in the middle. Those who failed to wear the star were subject to arrest and deportation, a fate that frightened most Jews into compliance even though the patch subjected them to restrictions, harassment, and isolation. Source: Abraham J. Edelheit, and Hershel Edelheit, History of the Holocaust: A Handbook and Dictionary (Boulder, CO: Westview Press, 1994), pp. 218, 239, 266, 448.
For more information about the history of the requirement that Jews wear a distinctive marking or sign, including during the Nazi period, see the entry "Badge, Jewish" in the Encyclopaedia Judaica, Volume 4 (Jerusalem: Macmillan, 1972), pp. 62-73.