You can still infer that the Nazi said something similar by looking at their expressions, the way they phrase things, and what they are surprised by.

The blonde is not surprised that the Nazi is quoted as an authority on fashion, but is surprised by the Nazi being a Nazi. The blue-haired person treats the Nazi quote as sufficient evidence to assuage the blonde's doubts.

If anything, you're interpreting this too narrowly. The blonde isn't anxious about the Nazi's opinion, but about the people that will see them at dinner. The comic suggests not just that the Nazi can be disregarded as a Nazi, but that the public perception of fashion is poisoned by Nazi standards and deserves to be defied.