Traditionally, dashi is made with only kombu and either bonito flakes (katsuobushi), sardines (niboshi) or shiitake. The bonito type is most common. Other fish parts, shrimp heads, crab, etc. wouldn't be part of the dashi (stock), but would be added later. In particular, a Japanese chef would never use sockeye trimmings due to the strong flavor. You can certainly make a delicious fish stock with all sorts of fish parts, it just isn't what most Japanese would consider dashi. Having said this, it is pretty rare in Japan, except at fairly upscale restaurants, for people to make their own dashi anymore. They typically use "hondashi" or some other powder that is just added to water. For those who make their own dashi, I would guess 99%+ use only kombu and bonito flakes.

Regarding the other comments about akamiso, I would concur with the poster who said it isn't a matter of quality just taste preference. I've been to extremely high sushi restaurants that serve miso soup made from white miso, and many that offer a choice.

Finally, it's possible the soup the OP had wasn't miso at all. Many people who aren't that familiar with Japanese cuisine assume all soup served at a sushi restaurant is "miso soup". I hope I'm not insulting anyone by pointing out unless it is cloudy, it doesn't have miso in it and some sushi restaurants serve clear soup (with various things in it) to finish the meal.