I would need to research further to confirm, but I have the feeling that the person who made that argument may have meant Erhard Milch.
From Wiki, it sounds that he was, indeed, high level brass:
In 1933, Milch took up a position as State Secretary of the newly-formed Reichsluftfahrtministerium ("Reich Aviation Ministry" – RLM), answering directly to Hermann Göring. In this capacity, he was instrumental in establishing the Luftwaffe, originally responsible for armament production
At the outbreak of World War II Milch, now with the rank of general, commanded Luftflotte 5 during the Norwegian campaign. Following the defeat of France, Milch was promoted to field-marshal (Generalfeldmarschall) and given the title Air Inspector General. Milch was put in charge of the production of planes during this time.
However, it appears that in answer to your very specific question, Erhard Milch did NOT indeed fit the specific definition you used.
His father was Jewish, which means he had at most 2 documented Jewish grandparents - the Nazi laws classified him as a Mischling ("crossbreed") and not a full Jew (3+ Jewish grandparents).
The Wiki provides the following detail (sources apparently from Benno Müller-Hill, Murderous science: elimination by scientific selection of Jews (1998), p. 26):
In 1935, Milch's ethnicity came into question because his father, Anton Milch, was a Jew. This prompted an investigation by the Gestapo that Göring squelched by producing an affidavit signed by Milch's mother stating that Anton was not really the father of Erhard and his siblings, and naming their true father as Karl Brauer, her uncle. These events and his being issued a German Blood Certificate prompted Hermann Göring to say famously "Wer Jude ist, bestimme ich" ("I decide who is a Jew")
An independent confirmation is quoted in a project from UCSB's class "for Prof. Marcuse's lecture course Interdisciplinary Perspectives on the Holocaust; UC Santa Barbara, Fall 2005". The quote is apparently from "Rigg, Mark. Hitler’s Jewish Soldiers, University Press of Kansas, 2002"
Field Marshal and State Secretay of Aviation Erhard Alfred Richard Oskar Milch’s "Aryanization" was the most famous case of a Mischling falsifying a father. In 1933, Frau Clara Milch went to her son-in-law, Fritz Heinrich Hermann, police president of Hagen and later SS general, and gave him an affidavit stating that her deceased uncle, Carl Brauer, rather than her Jewish husband, Anton Milch, had fathered her six children.… In 1935, Hitler accepted the mother’s testimony… (Rigg, 29)
He's still a good example of what most people whould consider "somewhat Jewish" person serving the Nazis at the top, but he does NOT fit the claim as you defined it in your question.
P.S. As a caveat, Erhard Milch was not in the army (as your arguer claimed) - he was in the air force (Luftwaffe). So either the person was mistaken slightly, or they meant a different person and my asnwer is wrong.