Magnesium stearate is hydrophobic — it repels water. During tablet and capsule manufacturing, it is typically blended with the other powdered ingredients immediately before compression or encapsulation, and because it is hydrophobic, it can form a thin coating over the surfaces of the other particles in the mix during that blending step. Pharmaceutical formulation science has studied this coating effect directly, because it has a real, measurable consequence: a hydrophobic coating on a tablet's particles can slow the rate at which water penetrates the tablet after it is swallowed, which in turn can slow the tablet's dissolution rate — how quickly it physically breaks apart and releases its contents into the digestive fluid.
A published study by Uzunović and Vranić, testing ranitidine hydrochloride coated tablets at varying magnesium stearate concentrations, found exactly this kind of effect: increasing magnesium stearate concentration in the tablet formulation was associated with a measurable slowing of the tablet's in vitro dissolution rate (Uzunović A, Vranić E. Effect of magnesium stearate concentration on dissolution properties of ranitidine hydrochloride coated tablets. Bosn J Basic Med Sci. 2007;7(3):279-283. PMID: 17848158). That is a real, peer-reviewed, mechanistically coherent finding, and it is the closest thing in the published pharmaceutical literature to the mechanism behind the consumer claim this post is checking.
It is also, on close reading, considerably narrower than the claim as commonly repeated. The study measured dissolution of a specific coated tablet formulation in a laboratory dissolution apparatus, at a range of magnesium stearate concentrations, for one specific drug. It did not measure, and was not designed to measure, whether nutrients from an unrelated ingredient are prevented from being absorbed across the human intestinal wall, and it did not test a capsule formulation of the kind used for Sodatide, where the mechanism of release (a dissolving capsule shell exposing a powder fill) differs from a compressed, coated tablet.