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In two recent papers published in MNRAS, Namouni and Morais (2018, 2020) claimed evidence for the interstellar origin of some small Solar System bodies, including i) objects in retrograde co-orbital motion with the giant planets, and ii) the highly-inclined Centaurs. Here, we discuss the flaws of those papers that invalidate the authors' conclusions. Numerical simulations backwards in time are not representative of the past evolution of real bodies. Instead, these simulations are only useful as a means to quantify the short dynamical lifetime of the considered bodies and the fast decay of their population. In light of this fast decay, if the observed bodies were the survivors of populations of objects captured from interstellar space in the early Solar System, these populations should have been implausibly large (e.g. about 10 times the current main asteroid belt population for the retrograde coorbital of Jupiter). More likely, the observed objects are just transient members of a population that is maintained in quasi-steady state by a continuous flux of objects from some parent reservoir in the distant Solar System. We identify in the Halley type comets and the Oort cloud the most likely sources of retrograde coorbitals and highly-inclined Centaurs.