How come an object that implements __iter__ is not recognized as iterable?

Let's say you work with a wrapper object:

class IterOrNotIter:
    def __init__(self):
        self.f = open('/tmp/toto.txt')
    def __getattr__(self, item):
        try:
            return self.__getattribute__(item)
        except AttributeError:
            return self.f.__getattribute__(item)

This object implements __iter__, because it passes any call to it to its member f, which implements it. Case in point:

>>> x = IterOrNotIter()
>>> x.__iter__().__next__()
'Whatever was in /tmp/toto.txt\n'

According to the documentation (https://docs.python.org/3/library/stdtypes.html#iterator-types), IterOrNotIter should thus be iterable.

However, the Python interpreter does not recognize an IterOrNotIter object as actually being iterable:

>>> x = IterOrNotIter()
>>> for l in x:
...    print(l)
...
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
TypeError: 'IterOrNotIter' object is not iterable

Whereas this works:

>>> x = IterOrNotIter()
>>> for l in x.f:
...    print(l)
...
Whatever was in /tmp/toto.txt

I don't understand why.