Using re-parameterized models to obtain interpretable point and interval estimates of C rests on standard assumptions for linear regression. Three important assumptions are (a) linearity of relations among variables, (b) equal measurement precision and equal intervals across the range of each variable, and (c) the observed range of X1 corresponding closely to its population range. First, regarding linearity, the cross-over point might be estimated in biased fashion if a linear model were fit to data with a quadratic relation between X1 and Y. Screening for nonlinearities in relations among variables would allow a researcher to evaluate the seriousness of this issue for data under consideration.
