The Palaeoarchean supracrustal belts in Greenland contain Earth's oldest rocks and are a prime target in the search for the earliest evidence of life on Earth. However, metamorphism has largely obliterated original rock textures and compositions, posing a challenge to the preservation of biological signatures. A recent study of 3,700-million-year-old rocks of the Isua supracrustal belt in Greenland described a rare zone in which low deformation and a closed metamorphic system allowed preservation of primary sedimentary features, including putative conical and domical stromatolites' (laminated accretionary structures formed by microbially mediated sedimentation). The morphology, layering, mineralogy, chemistry and geological context of the structures were attributed to the formation of microbial mats in a shallow marine environment by 3,700 million years ago, at the start of Earth's rock record. Here we report new research that shows a non-biological, post-depositional origin for the structures. Three-dimensional analysis of the morphology and orientation of the structures within the context of host rock fabrics, combined with texture-specific analyses of major and trace element chemistry, show that the 'stromatolites' are more plausibly interpreted as part of an assemblage of deformation structures formed in carbonate-altered metasediments long after burial. The investigation of the structures of the Isua supracrustal belt serves as a cautionary tale in the search for signs of past life on Mars, highlighting the importance of three-dimensional, integrated analysis of morphology, rock fabrics and geochemistry at appropriate scales.