Parametric strong lensing studies of galaxy clusters often display "misleading features". This is the case in the galaxy cluster Abell 370. Using strong lensing techniques, it has been described parametrically by a four dark matter clumps model and galaxy scale perturbers, as well as a significant external shear component, which physical origin remains a challenge. The dark matter distribution features a mass clump with no stellar counterpart and a significant offset between one of the dark matter clumps and its associated stellar counterpart. In this paper, based on BUFFALO data, we begin by revisiting this mass model. We find a four dark matter clumps solution which does not require any external shear and provides a slightly better RMS compared to previous models. Investigating further this new solution, we present a class of models which can accurately reproduce the strong lensing data, but whose parameters for the dark matter component are poorly constrained. We then develop a model where each large scale dark matter component must be associated with a stellar counterpart. This model is unable to reproduce the observational constraints with an RMS smaller than 2.3", and the parameters describing this dark matter component remain poorly constrained. Examining the total projected mass maps, we find a good agreement between the total mass and the stellar distribution, both being bimodal. We interpret the "misleading features" of the four dark matter clumps mass model and the failure of the three dark matter clumps mass model as being symptomatic of the lack of realism of a parametric description of the dark matter distribution, and encourage caution and criticism on the outputs of parametric strong lensing modelling. We briefly discuss the implications of our results for using Abell 370 as a gravitational telescope.