I think is is just a more compelling narrative that Hitler was rejected because he didn't make crazy incomprehensible "my 5-year old son could have made that!" avant-garde art. But note that cubism was barely invented in 1907, and the academy represented a conservative view of art. If you look at the kind of art Hitler endorsed when he came to power, it was actually pretty close to the academy style.

That is a compelling narrative I guess. I had always associated that period of Viennese art with that of Gustav Klimt, who seems to have been reasonably successful in that period. He probably didn't represent the conservative views of the academy as you said.

No Klimt represented the "Secession" movement which at that time was in opposition to the establishment and the academy. According to wikipedia: "in particular, opposing the domination of the official Vienna Academy of the Arts, the Vienna Künstlerhaus, and official art salons, with its traditional orientation toward Historicism. " https://en.wikipedia.org/wiki/Vienna_Secession

I think Nazims famous opposition to modern art have been conflated with Hitlers own rejection from the academy. He wasn't rejected due due different genre preference, but because he wasn't good enough in drawing anything beside architecture.