Most fascist dictatorships have had large privatizations and all have favored corporations in economic policy. You act like business-state collaboration under fascism was unique to the nazis, but it was also central to fascist Italy, Francoist Spain, and right-wing dictatorships like those of Pinochet or the military in Brazil.
Fascism happens when capitalism is in crisis because it’s better for the corporations than socialism would be. Both Italy and Germany had strong socialist movements in the years before fascists came to power, and fascists are consistently funded by a business community that fears losing everything it has. The fascist emphasis on the state, nationalism, and war, is only because it’s required to suppress organized labor.
I think “convinced of” is more correct, but both phrases work. Could also say “convinced on”.