The behavior of stress through a cross section of a thickness is neither linear nor quadratic through the entire thickness. So, if you only have one element across the thickness you are not adequately calculating these internal stresses. This page (How to create a good quality FEM model? - MSC Apex) gives a graph showing how the stress through the thickness changes with different numbers of elements across the thickness.
It's an old rule of thumb for accurate prediction of bending stresses in FEA so I don't think you'll find a strong physical basis for an answer.
If you are running Simulation then you already have access to a virtual testing tool, so the best recommendation I can make is test yourself a model with 1, 2, 3 elements etc through the thickness and see if it actually affects your results in practice. Very simple to duplicate a study and try a run with different level of mesh refinement.
Mesh refinement required is highly dependent on the load case and geometry. In many cases a single element through the thickness may suffice, in other cases you may need many elements through the thickness.
The practice of mesh refinement and checking for mesh convergence or a "mesh independent" solution is one step of the process for seeking highly accurate results from FEA.
Remember there are many other potentially larger sources of error, such as using incorrect boundary conditions. I would argue it's much more important to carefully consider your assumptions for the analysis. Mesh refinement can be easily fine tuned later on.
it is generally advised to have minimum 3 elements of mesh size along the thickness of the part and based on this select the mesh size and then do a mesh convergence...