Roseanne's claim was that she didn't even know Valerie Jarrett was African-American, which, is actually pretty believable if you ask me. First off, to probably 95% of Americans "Valerie Jarrett" is just a name from the nightly news and not someone they could ever actually put a face to. "Senior Advisor to the President" and "Director of the Office of Public Engagement and Intergovernmental Affairs" aren't exactly offices that attract a lot of attention from the majority of people...
I mean, for crissakes, I'm a huge politics junkie who can rattle off the names of the current and the last five people who held the Senior Advisor to the President post -- Jared Kushner, David Axelrod, Barry Jackson, Valerie Jarrett, Karl Rove, Sid Blumenthal -- but I'll be damned if I could pick any of them out of a line up. Okay, maybe Kushner... although, honestly, he looks pretty much like every other middle-aged Yeshivot lawyer on the planet. Roseanne's tweet was mocking her appearance, so obviously she knew what Jarrett looked like... But did she think Jarrett looked African-American? She says she didn't, and honestly, I believe her. Jarrett has very fair skin and routinely self-identifies as "Iranian-American" or "Iranian" in interviews. A lot of people might assume she's Persian.

Valerie Jarrett is on the left (pun not intended).
Furthermore, both of her parents are apparently bi-racial themselves. Apparently, Jarrett was on a 2014 episode of PBS's show Finding Your Roots, which used DNA testing to show that Jarrett is of 49% European, 46% African, and 5% Native American. So if we're going to play stupid identity politics games, then Jarrett is actually more "white" than she is "black."
TL;DR: The whole shit storm unleashed was dumb.