I suppose the example that I always think of is Japan. They had universal suffrage, a healthy democracy in the 1920s. Yet the military seized power in the 1930s and directed the nation into armageddon. What makes Germany's military any different, given their lack of respect for democracy that we saw in OTL?
There were some critical differences. Japan's constitution and laws explicitly said that the Army Minister must be filled by an active duty general. This gave the Army a de facto veto on the formation of any government because if it refused to provide a minister, there couldn't be a government. The Army Minister also reported directly to the Emperor, not the Prime Minister so the army was more or less autonomous. This was very different than the situation in Germany.
The second difference is that much of Japan's adventurism was a result of the junior officers in China deciding to cause problems (the various "incidents") to force the government (and top army brass) to follow its lead. It is hard to imagine any German officer in the field so unilaterally creating their own orders or acting in defiance of their own superior officers.
Both differences were instrumental in dismantling civilian rule in Japan, and really did not have counterparts in Germany.
In addition, after the Kapp Putsch the military generally had a good relationship with the Weimar Government. They might not have liked Weimar, but Weimar was generally friendly to the military's desires. The greater problem in Germany was the general right wing violence, often found outside the military, and that the judiciary and police who were dominated by conservatives and who rarely went after and punished right wing political criminals.