https://docs.python.org/3/library/inspect.html#inspect.isfunction says this:

"""
inspect.isfunction(object)
Return True if the object is a Python function, which includes functions created by a lambda expression.
"""

Emphasis on the "Python function", as in, something written in Python using a `def` statement or a `lambda` expression. If isfunction returns True, you can presumably access function-specific implementation details like the functions's f.__code__ attribute. If you need to check for "anything that works as a function", you can use `callable()`:

>>> callable(lambda: 2)
True
>>> callable(abs)
True
>>> def f(x): return x
>>> callable(f)
True

I'm not an expert on the inspect module, but I'm guessing it's not worth breaking backwards-compatibility to change this behavior.

Would extra emphasis in the documentation have been helpful for you, or were you mostly attempting to rely on the function's name?