I just had morning tea and our geologist who specialises in old rocks and early life was in the tea room (having a break from hand-picking zircons for dating). He hadn't heard this specific claim but found it very believable. He says that the 3.4-3.5Ga (billion years ago) date has been about for decades. Generally in the Pilbra the dating is very good and the debate revolves around interpretation of the structure. In that context the carbon-isotope data is very important (but of course isotope data is always important
).
BTW in the display cases just down the corridor is a stromatolite dated to 3.45Ga and a banded iron formation (BIF) dated to 3.7Ga. The BIF contains iron oxide and that oxygen was formed by photosynthesis. Hence: life at 3.7Ga.