There is also a deterministic method that solves the equations so that the result is an exact match with the data. Why not use that?
That works if you are using noiseless data, i.e. exact measurements with no error. If there is an error on the data and a particular model fits the data (with error) exactly (each data point), then you are 'fitting the noise' which must mean the model includes too many parameters than can be justified by the data and the model must therefore be wrong.