The ∼3700 Ma and 3800 Ma meta-volcanic and -sedimentary rocks in the Isua supracrustal belt (Greenland) were affected by heterogeneous ductile deformation under amphibolite facies conditions (∼500-650 °C), and variably modified by secondary silica and carbonate mineralisation deposited from diagenetic and metasomatic fluids. Rare low-deformation areas preserve original volcanic features - submarine basaltic pillows and sedimentary features - including bedding. These are best-preserved in two dimensions on flat- to moderately-inclined outcrop surfaces, but invariably are tectonically-stretched along a steeply-plunging third dimension, through stretching in the direction of fold axes; a style of deformation found throughout Earth's history. There is a debate about whether rare relicts of ∼3700 Ma stromatolites preserved in metadolomites that formed in a shallow marine setting (Nutman et al., 2016) represent bona fide biogenic primary structures fortuitously preserved in low deformation, or whether these structures are manifestations of deformation combined with non-biogenic deposition of secondary carbonate (Allwood et al., 2018). Here, we critically test the primary nature of the sedimentary rocks hosting the proposed stromatolites and also the veracity of the proposed stromatolites, by addressing the following questions: (i) Are the rocks an in situ outcrop of known age, or displaced blocks of unknown age or origin?; (ii) How much of the carbonate is of an originally sedimentary versus a secondary (i.e., metasomatic - introduced) origin?; (iii) Is the seawater-like REE + Y (rare earth element and yttrium) trace element signature carried definitely by carbonate minerals and therefore diagnostic of a cool, surficial sedimentary system?; (iv) Are the proposed stromatolites consistent with biogenicity in terms of their geometry and fine-scale layering, or could they be the product of soft sediment or structural deformation (compression in folding)? The answers to these questions, which combine diverse observations from geologic context, geochemistry and stromatolite morphology show that the weight of evidence is consistent with a biogenic origin for the stromatolites formed in a shallow water setting and are inconsistent with formation entirely through inorganic processes.