Indeed. Hitler was quite to the left by American definitions of the term.
Hitler is often referred to as 'right wing'. Historically, 'right wing' in early twentieth century European politics meant he was a 'right wing' socialist. A 'right wing' socialist according to Lenin was one who wanted socialism but didn't want violent revolution to achieve it (see: Lenin and Right Wing). Right wing socialists were also interested in national socialist parties, rather than socialist parties owing allegence to international socialist or communist organizations that Lenin espoused.
The mainstream media conveniently leave out the socialist part when calling Hitler 'right wing'. Nazi principles are basically socialist (see points 11, 13, 17, 23, and 25 of Hitler's 25 Points).
A 'right wing' European socialist does not equate to a 'right wing' American politician. If anything, the Nazi party was closest in ideology to the left wing of the Democrat Party, some of whom are nothing but socialists.