From your article:
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.
FYI: Stromatolites are still being formed in some parts of the world.
As Allwood seems to be saying is that they look like stromatolite fossils but the time period would seem to suppose that life developed before and survived the Late Heavy Bombardment. That’s a hard question to answer.
Living Stromatolites, western Australia:
Stromatolite Fossils - Trezona Formation, South Australia, about 1 billion years old:
What's certain is that some stromatolite fossils look very old indeed, over 3 billion years.
So the question is whether those very oldest fossils are also stromatolites, or just some non-organic rock formation.