Contrary to a widespread opinion, horizontal gene transfer (HGT) between distantly related microorganisms (such as Bacteria and Archaea) has not been demonstrated to occur on a large scale. Except for transfer of mobile elements between closely related organisms, most alleged HGT events reflect phylogenetic discrepancies that can be explained by a variety of artefacts or by the differential loss of paralogous gene copies either originally present in the Last Universal Common Ancestor (LUCA) to the three Domains (a sophisticated, genetically redundant and promiscuous community of protoeukaryotes), or created by duplications having occurred at later times. Besides, (i) there is no experimental evidence for the facile acquisition of foreign DNA between distant taxa and (ii) important biological constraints operate on the phenotypic success of genetic exchange at several levels, including protein-protein interactions involved in metabolic channelling; stable integration and expression of foreign DNA is, therefore, expected to require strong selection. Explaining phylogenetic discrepancies by artefacts or loss of paralogs does not eliminate difficulties in retracing species genealogy but maintains the picture of a universal tree of life, HGT between distant organisms being reduced to a trickle. We illustrate our thesis by the phylogenetic analysis of carbamoyltransferases, a family of paralogous proteins. Among higher eukaryotes HGT appears of limited scope except in asexual organisms. We suggest that meiotic sexuality (a hallmark of eukaryotes) emerged in the genetically redundant and protoeukaryotic LUCA as a molecular identity check providing a defence mechanism against the deleterious effects of HGT.