In the article the term "organic" isn't used at all:

  > The dating seems about right, said Abigail Allwood , a NASA
  > astrobiologist who found the previous oldest fossil, from
  > 3.48 billion years ago, in Australia. But Allwood said she is
  > not completely convinced that what VanKranendonk's team found
  > once was alive. She said the evidence wasn't conclusive enough
  > that it was life and not a geologic quirk.
  > 
  > "It would be nice to have more evidence, but in these rocks
  > that's a lot to ask," Allwood said in an email.