Here's a link that says as much:
The message formally accepted the Potsdam Declaration but included the proviso that “said Declaration does not comprise any demand which prejudices the prerogatives of His Majesty as sovereign ruler.” When the message reached Washington, President Truman, unwilling to inflict any more suffering on the Japanese people, especially on “all those kids,” ordered a halt to atomic bombing, He also wanted to know whether the stipulation regarding “His Majesty” was a deal breaker. Negotiations between Washington and Tokyo ensued. Meanwhile, savage fighting continued between Japan and the Soviet Union in Manchuria.
What do you think?
That extraordinarily poorly-written and incomplete description of the "negotiations" mischaracterizes them. Even so, the headline should make it clear that the authors did not intend anyone to think the US had accepted a conditional surrender.
The US flatly reasserted that full unconditional surrender would be required — they rejected the "proviso." A few days later, the Japanese offered up a surrender that no longer included any exceptions.
You can read the surrender documents here.
Ultimately the US Occupation agreed (later) to grant the Emperor some continuance (albeit in a reduced form), but that was their choice to do so; the Japanese had agreed to whatever the US decided on this issue.