"May have been" = "we have no evidence of it having influenced them." It is not a strong claim and not one that historians have ever given any credence.

In that thread, /u/riograndekingtrude 's comment is pretty good. I would disagree on several points (e.g. the idea that the Soviet declaration of war was not a surprise — there is a lot of hard evidence that it was a surprise, and that the cornerstone of both the "dove" and "hawk" positions was keeping the Soviets neutral). Some of the timing is ambiguous in this version because it doesn't specify time zones — the Soviet invasion of Manchuria began around 1am Tokyo time on the morning of August 9th, not the afternoon. (So the SWC was woken up in the night and told about the Soviet invasion, had a meeting scheduled for 10:30am, and then the Nagasaki bombing news came.)

Anyway, the general gist of it, which is what makes it good, is that there was no single little thing like "oh some POW told us the US might have 100s of bombs." This was a much bigger and complicated process than that, and the atomic bombs were one aspect of what was going on at the time. The notion that dubious, unverifiable, unlikely intelligence from one captured pilot would have been the straw that broken the camel's back is silly.

(If the US had hundreds of atomic bombs, why didn't it drop them earlier in the war? Why save up hundreds and then drop one or two? It doesn't make any sense. A more likely guess is either that the US only had one, or that they had a small number, and that they maybe had a production system for producing more over time. The latter parts were correct — the US had a small number and could produce more as time went on.)

The atomic bomb was a serious blow for the Japanese Empire but it was not the decisive one: Japanese war cabinet was prepared to face a land invasion that would prove very difficult for american troops; moreover, even if the country had lost its Pacific domains, in Manchuria the Kwantung army, one of the elite units of the Japanese army counting 1,5 million personnel, was intact, rested, supplied and ready to fight. on n the early days of August 1945, prince Konoye Fuminaro was sent to Moscow in order to have a better understanding of Soviet feelings towards Japan and to try to convince USSR to stay away from the conflict; however, he wasn't allowed to enter the country and the Soviet Union declared war to Japan on the 9th August, crushing the Kwantung army in few days and occupying all Manchuria. This was the final blow for the Japanese government, the moderate forces succeeded in convincing the Emperor to accept unconditional surrender.

Sources: my bachelor degree dissertation; I know that this accounting is far from accurate, I just wanted to outline the situation in order to let OP understand it :).

As a further reading I would suggest:

• Wilson D. Miscamble, from Roosevelt to Truman: Potsdam, Hiroshima and the Cold war.
• the Cambridge history of Japan vol.6
• Robert A. Paper, why Japan surrendered, in International security vol.18 n°2, 1993.
• Michael Schaller, the American occupation of Japan, the origins of cold war in Asia (this available also in kindle format)

Perhaps it was just a compiling of all things that had happened. The Japanese had been pushed from the East Pacific all the way back to their own shores.
Everything they had tried had pretty much failed. They no longer had enough powder to operate AA guns. They would have the crews put in enough powder just to make a noise to give the people the illusion that they were fighting back. Few fighters were left to go up after the numerous American bombers and ships.

Then two cities were destroyed in seconds by two bombs. A newly captured soldier says they have hundreds more. And now the Soviets have declared war.

The information the new POW lied about may not of stopped the war but, gave the leaders something to think about.