Are "{Binding Path=.}" and "{Binding}" really equal

In my WPF project, I have a ListBox that displays items from a List<string> collection. I wanted to make the text of these items editable, so I wrapped each of them in an ItemTemplate with a TextBox (might not be the best way, but I'm new to WPF). I was having trouble simply binding the TextBoxes' Text property to the value of each item. I finally stumbled upon an example using a single dot or period for its Path property ({Binding Path=.}):

<ListBox ItemsSource="{Binding ElementName=recipesListbox,Path=SelectedItem.Steps}">
    <ListBox.ItemTemplate>
        <DataTemplate>
            <TextBox Text="{Binding Path=.}"/>
        </DataTemplate>
    </ListBox.ItemTemplate>
</ListBox>

However I don't understand why simply using {Binding} didn't work.

It raised a "Two-way binding requires Path or XPath" exception, as according to Microsoft:

[...] a period (.) path can be used to bind to the current source. For example, Text="{Binding}" is equivalent to Text="{Binding Path=.}"

Could someone shed light on this ambiguous behavior?

EDIT: Moreover, it seems {Binding Path=.} does not necessarily give two-way binding, as modifying the text and moving the focus does not update the underlying source (the same source has also properties displayed and successfully modified on a DataGrid control). I'm definitely missing something here.

The point of the exception presumably is that you cannot two-way bind a binding-source itself, so it tries to prevent you from creating a binding which does not behave the way you would want it to. By using {Binding Path=.} you just trick the error detection.

(Also it's not unheard of that documentation is erroneous or inaccurate, though i do like the MSDN documentation a lot in general as it usually does contain the crucial points one is interested in)

The documentation states that {Binding} is equivalent to {Binding Path=.}. However it is not equivalent to {Binding Path} as you have typed. If you include the Path property, you must assign it to something, be it Path=. or Path=OtherProperty.