I suppose that the s-curve with 3 parameters that the author is talking about is the logistic function. In general, if you consider a differentiable function of three parameters and try to determine and interval for the values of the parameters of that model then the length of that interval is bound by the ratio of the error in the data over the derivative with respect the parameter. For example estimating the parameter k (wikipedia logistic growth rate) with points such that x near x0 = (wikipedia midpoint of the sigmoid) is hard, since the derivative of the function with respect to k at x=x0 is zero. So mathematically this seems to be a well known fact when one try to estimate parameters from datapoints.