Becasue it is indeed what happened?

Yes in the days between the double hammers of the Soviet Union's joining the war a few hours before the bombing of Nagasaki, the tension over the status of the Emperor in a post-war world was still not resolved. And even before then there were voices in Allied governments who suggested even an informal softening on that point could quicken the end of the war, though Truman was not moved, even when Churchill was one of those voices(though he would be out of power following the British election in July).

With the end so near in essence those voices, in part centered around Secretary of State Byrnes as noted in your link, were able to sway Truman(who also was experiencing something like shock after more fully realizing just what a nuke can do to a city, not that it was much different from mass conventional attacks), while some conventional bombing continued to keep pressure up.

So yes the surrender terms Japan and the Allied powers agreed too was based on the Potsdam decleration that demanded unconditional surrender but with the "clarification" or however one might want to term it, that the Emperor was not going to be summarily removed by the occupation force.

For some additional reading on the end of the war there are several places you might look at!

Hasegawa's "Racing the Enemy" is a seminal work looking at the decisions around when and how to use the bomb, reacting to it, and the competing motivations of different participants, on all sides with more attention paid to the USSR's role than traditionally was given. "Downfall" by Richard Frank is another popular work who comes to the conclusion of the bomb's effectiveness in ending the war before the time for invasion arose, though the very quiestion of if an invasion would go forward and if Japan holds out that long were far from certain in the moment. Ian W. Toll's "Twilight of the Gods" is the 3rd part of his general Pacific War trilogy, covering the last 2 years of the war, I would heartily recommend his series as a good, if rather American centric, look general history of the Pacific War.