Eukaryotic organelles depend on nuclear genes to perpetuate their biochemical integrity. This is true for mitochondria in all eukaryotes and plastids in plants and algae. Then how do kleptoplasts, plastids that are sequestered by some sacoglossan sea slugs, survive in the animals' digestive gland cells in the absence of the algal nucleus encoding the vast majority of organellar proteins? For almost two decades, lateral gene transfer (LGT) from algae to slugs appeared to offer a solution, but RNA-seq analysis, later supported by genome sequencing of slug DNA, failed to find any evidence for such LGT events. Yet, isolated reports continue to be published and are readily discussed by the popular press and social media, making the data on LGT and its support for kleptoplast longevity appear controversial. However, when we take a sober look at the methods used, we realize that caution is warranted in how the results are interpreted. There is no evidence that the evolution of kleptoplasty in sea slugs involves LGT events. Based on what we know about photosystem maintenance in embryophyte plastids, we assume kleptoplasts depend on nuclear genes. However, studies have shown that some isolated algal plastids are, by nature, more robust than those of land plants. The evolution of kleptoplasty in green sea slugs involves many promising and unexplored phenomena, but there is no evidence that any of these require the expression of slug genes of algal origin.