That's an excellent question.   To be honest, I don't think this has been tested in great detail, with the main issue being "when can you truly tell that you've used too many parameters".  
We typically rely on "when adding a variable doesn't improve reduced chi-square" as that measure.  But, the definition of reduced chi-square that we use includes a value for N_idp already, so we're more or less *imposing* the Stern rule.

I think lots of us have observed cases where the Stern rule is definitely optimistic.  And that might be understandable because the Stern rule doesn't include a separate measure of the noise in the data, or what the distribution of "the effect" of the parameters would be on the signal.    That is, one can always increase the R range to 20 Angstroms, and so increase N_idp.  But if you're trying to fit 25 variables for the part of the signal between 1.5 and 2.5 Ang, there is probably going to be very hard to get good measures of all 25 variables.   The Stern rule sort of doesn't account for this, except in the sense of giving guidance.

It would be interesting the revisit this with a better statistical treatments of information.  There are, for example, statistical values like the Akaike Information criterion (https://en.wikipedia.org/wiki/Akaike_information_criterion) and related values that might be useful for better understanding when one is using too many parameters. 

--Matt