That statement, to the best of my knowledge, is false. There was never a free election in Austria to anoint Hitler. The Nazis seized Austria militarily in 1938 with little trouble, having undermined the previous Austrian regime internally for years before sending the troops in. They arrested the Austrian chancellor and sent him to a concentration camp. There was some opposition to the Nazi takeover within Austria (aided by German emigrees) but it never manifested itself to the level where it could muster any military resistance.
Regrettably, the statement about the supposed election mars an otherwise credible article by Ms. Werthmann.
Austria was annexed to the German Third Reich on 12 March 1938. There had been several years of pressure from Germany and there were many supporters within Austria for the “Heim ins Reich”-movement, both Nazis and non-Nazis. Earlier, Nazi Germany had provided support for the Austrian National Socialist Party (Austrian Nazi Party) in its bid to seize power from Austria’s Austrofascist leadership. Fully devoted to remaining independent but under considerable pressure from both German and Austrian Nazis, the Chancellor of Austria, Kurt Schuschnigg, tried to hold a referendum to ask the Austrian people whether they wished to remain independent or merge into Germany. Although Schuschnigg expected Austria to vote in favour of maintaining autonomy, a well-planned coup d’etat by the Austrian Nazi Party of Austria’s state institutions in Vienna took place on 11 March, prior to the referendum which was cancelled. With power quickly transferred over to Germany, Wehrmacht troops entered Austria to enforce the Anschluss. The Nazis held a plebiscite — asking the people to ratify what had already been done — within the following month, where they claim to have received 99.73% of the vote.