Earlier quoted context omitted.
You misunderstand - the belief is not that the US could have won the war even without the bombs, but that "bombs vs. invasion" was a false dichotomy, and that Japan would have unconditionally surrendered around the same time without the bombs, or perhaps even sooner had the conditional surrender they were already seeking been on the table.
The Japanese offered to surrender if they could continue to control their captured territories, essentially continuing to rape China. That’s a hell of a condition to allow them.
To this end, Stalin and Molotov strung out the negotiations with the Japanese, giving them false hope of a Soviet-mediated peace. [..] The Japanese would have to surrender unconditionally to all the Allies. To prolong the war, the Soviets opposed any attempt to weaken this requirement.[56] This would give the Soviets time to complete the transfer of their troops from the Western Front to the Far East, and conquer Manchuria, Inner Mongolia, northern Korea, South Sakhalin, the Kuriles, and possibly Hokkaidō - https://en.wikipedia.org/wiki/Surrender_of_Japan#Soviet_inte...
However, the Japanese presented no formal terms, because details were to be worked out by negotiation. - https://www.quora.com/When-Japan-offered-conditional-surrend...
Edit as reply due to rate limit:
The article you linked doesn't support the claims you made about Japan's conditional surrender. The closest it comes is "Anami wanted retention of the emperor, self-disarmament, no foreign occupation, and trial of any Japanese war criminals by Japan itself". But that is what Anami wanted, not what was written down in some final, take-it-or-leave-it offer. And that's from before the Soviet declaration of war.
In fact the article basically contradicts your claim about the necessity of the bombs:
> The bomb played a part in Japan’s surrender, but it may not have been necessary, he said. Had the U.S. drawn Stalin into publicly supporting the Potsdam Declaration’s unconditional surrender demand, Japan might not have held out hope for a Soviet-brokered deal. Had it guaranteed the emperor’s position, Japan might have surrendered earlier, Hasegawa said, though this is yet another point that draws endless historical debate.
> “Other alternatives were available, but they were not explored,” Hasegawa said.
Choosing the bombs over merely exploring other options is rather damning, don't you think?