This actually isn't true for some types of farmed fish, like Norwegian salmon, but it varies by area and by company.
The industry is looking into alternatives like insects, and typically 30-40% of the feed now comes from vegetable proteins and oils.
On the other hand, farmed Faroese salmon (just next door) has a much higher % of wild-caught fish in its feed, which contributes to the high omega 3 content of Faroese salmon.