Not only is it not common knowledge, it's not true. The SS was a political miltia. It was not selected for eliteness, it was selected for their zealotry to the Nazi cause.
The fundamental difference between the Wehrmacht and the SS was that the former was sworn to defend Germany from all foes, inside and out; the latter was sworn to defend Adolf Hitler. In effect, they were initially recruited as Hitler's personal bodyguards, and expanded from there into a semi-autonomous and semi-elite (less of the latter as time went on) branch of the military, because Hitler had legitimate concerns that his own army would depose or kill him....which they attempted on at least 3 occasions.
To try to put the Budapest issue into context, Hungary had repeatedly refused Hitler's demands to close the borders to refugees from Poland, Czechoslovakia, and a few of Hitler's other early conquests, and Budapest became a temporary home for well over 100,000 such refugees fleeing from persecution at the hands of the Nazis. The Germany army carried out several military operations through Hungary before occupying the country directly, and within Hungary as the Soviets advanced, but several SS units were stationed in Budapest on account of those refugees, and that primarily non-military operation was stepped up near the end before the Soviets could interfere. Those SS units were not there to fight the Soviets, not there to protect Hungary, and not welcomed by the Hungarian government (at least those who hadn't already been arrested or killed by the Nazis) or most of the general population. It's not permitted to discuss that operation in further detail here on the forum. Calling that "defense of Hungary" is beyond wrong, and using that as an example of "badass" conduct is insulting. Note, I'm not from there, in case you're attributing this to educational propaganda, although several of my great-great-grandparents were, and I visited the country once.
Many of the old Prussian-style German generals, back when an officer could refuse an order on moral grounds, could be considered "badass"; many of the "just following orders" latecomers were just "bad" in the wrong way. At the start of the war, there were still enough of the "old guard" to retain Germany's "badass" status; by the end, that was mostly dead, discredited, or otherwise out of favor with the new leadership. Sadly, it's that late politically polarized group who seem to draw all of the enthusiasm, despite making a rather poor showing in combat, rather than the old group who almost succeeded in defeating the world, and hated the "Little Corporal" who constantly interfered with the professional running of a war.
While India's decision not to exploit the UK's crisis may be admirable, I wouldn't put it in the "badass" category. A few of the Gurkha units (if I got the spelling right) had a fearsome reputation, and could certainly be considered "badass", but I wouldn't extend that to their entire military or country. Finland's determined struggle against the Soviets would seem to make them a much better candidate for the title.
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