The docs are correct as-is.  This is a documented and tested behavior.

    >>> from heapq import nsmallest
    >>> list(nsmallest(3, ['larry', 'georg', 'raymond', 'guido', 'tim'], key=len))
    ['tim', 'larry', 'georg']

The C implementation doesn't have a key-argument.  That behavior gets added downstream in pure python in Lib/heapq.py which wraps the C-function and adds the additional behavior.