This is alternative history, not real history. Remember, there was an attempted coup even after the first bomb to prolong the war. The Japanese leadership at the time were very zealous verging on religious zeal. One of the things that got them to eventually give up was a captured US fighter pilot that (under threat of death) told the Japanese that the US had 100s of atomic bombs. This was a lie but he didn't know that and just was trying to get the insane intelligence agent to not cut his head off (literally). There were other factors too. The USSR invading Manchuria for example. Also the US was in the process of ringing the home islands with 50 fleet carriers (the big ones, 50kt displacement) which would have been able to bomb Japan at will. Even with all of this, there was a significant faction of Japanese leadership who wanted to fight on.

These claims are more about politics than anything. Its an attempt to retcon history to vilify the US. The Japanese had never been invaded and that was a huge point of pride. They were training the civilians for a guerrilla war. Just because you can find a person in the Japanese government who wanted to surrender at that point (and there were) doesn't mean that's the decision that would have been taken.

PS That 3rd point is especially specious...if it were true, no 2nd bomb would have been used. PPS Stuff like this is why historians don't like nor will engage with hypotheticals or the alternative history folks. Its clearly politically motivated, not a good faith attempt to understand history.