Different formulas relating measurable fragment isotopic observables to the symmetry energy of excited nuclei were proposed and applied to the analysis of heavy ion collision data in the recent literature. In this article, we examine the quality of the different expressions in the framework of the McGill canonical thermodynamic model (CTM). We show that even in the idealized situation of canonical equilibrium and in the absence of secondary decay, these formulas do not give a precise reconstruction of the symmetry energy of the fragmenting source. However, both isotopic widths and isoscaling appear very well correlated to the physical symmetry energy.