'Perceived' is correct, as the other option was conditional surrender of Japan. But it sounds much nicer, and is better for morale, to say the bombs or an invasion were the only possibilities.

Sources:

https://www.washingtonpost.com/opinions/five-myths-about-the...

https://www.atomicheritage.org/history/debate-over-japanese-...

https://mises.org/library/hiroshima-myth