I would add two points. First, the main German socialist party, the SDP, essentially abandoned the goal of state ownership of the means of production in the late 19th Century. Basically what happened is that Bismarck and the conservatives agreed to establish a cradle to grave welfare state if the socialists would drop nationalization. So, the NAZI platform is not markedly different than mainstream German socialism on this issue.
The second point is to look at who elected the NAZI's. The electoral maps of the last two German elections before the NAZI dictatorship was elected showed conservative support roughly static, winning primarily traditionally conservative constituencies in the south and west. The dramatic change was the majority of socialist constituencies which flipped from SDP to NAZI. Socialist voters put the NAZI's in power.