Placing cursor on text with `display' property

[Eli Zaretskii]

The ELisp manual says, where it describes the `cursor' text property:

     Normally, the cursor is displayed at the end of any overlay and
     text property strings present at the current window position.

But this is false, isn't it?  AFAICS, we display the cursor on the
_first_glyph_ produced from the overlay or text property string that
is present in the buffer at point.  Did I miss something?