I think you are engaging in a equivocation fallacy here. "Share" does not imply they didn't create the story, only that they were the sources of the information. ie: "to give specific users access to (online content), as by posting it on a social-media website or sending it as an email attachment: "
Originally Posted by mican333
The context of the article clearly implies that they are the primary source from which the conspiracy started, that it was their emails that started the widespread discussion. '
It was not until April 2008, at the height of the intensely bitter Democratic presidential primary process, that the touch paper was properly lit.Second Source
An anonymous email circulated by supporters of Mrs Clinton, Mr Obama’s main rival for the party’s nomination, thrust a new allegation into the national spotlight — that he had not been born in Hawaii.
That Clinton staffers were the source of the original distribution that led to widespread media attention doesn't even seem controversial:
Politico explained it in detail, hell even factcheck.org notes that it started on the left. The lawsuit that caught Trump's real attention and which he cited for a while was from a former Clinton campaign operative.
We also should point out that Sydney Blumenthal, long time Clinton operative is mentioned in the first link and cited frequently as a source of information in the early days of this conspiracy theory.
former McClatchy Washington Bureau Chief James Asher tweeted Friday that Blumenthal had “told me in person” that Obama was born in Kenya.
“During the 2008 Democratic primary, Sid Blumenthal visited the Washington Bureau of McClatchy Co.,” Asher said in an email Friday to McClatchy, noting that he was at the time the investigative editor and in charge of Africa coverage.
“During that meeting, Mr. Blumenthal and I met together in my office and he strongly urged me to investigate the exact place of President Obama’s birth, which he suggested was in Kenya. We assigned a reporter to go to Kenya, and that reporter determined that the allegation was false.
“At the time of Mr. Blumenthal’s conversation with me, there had been a few news articles published in various outlets reporting on rumors about Obama’s birthplace. While Mr. Blumenthal offered no concrete proof of Obama’s Kenyan birth, I felt that, as journalists, we had a responsibility to determine whether or not those rumors were true. They were not.”