ok, there may be use cases for calculating a variance estimate in such situations, but IMHO what you are trying to do is to abuse a function which is not documented to be made for the purpose and then complain that it does not behave correctly.

The *documented* use of the mu argument is to avoid redundant calculations of the mean of data!
With just one argument, how would you know whether the user wants this documented functionality or the undocumented one ?

Your suggestion of just omitting the correction means that every user who wants the documented functionality gets a potentially imprecise result.
Another potential approach may be to correct the correction term based on the mean calculated from data, but such a calculation would be absurd given the documented functionality.

In case the statistics module is going to use exact representations of internal results in 3.5, the error adjustment would become obsolete anyway (see http://bugs.python.org/issue20499) and pvariance could be abused just as you suggest.
In this case, this usage could be sanctioned in the form of a recipe ?