(invisible-p (point)) has already been tested in the previous line, but it
only tests that there is a text property, not actual invisibility:
(defun invisible-p (pos)
  (get-text-property pos 'invisible))

If the text property `invisible' has another symbol than t as value and
`buffer-invisibility-spec' is a list (which is the case in dired, see
below), then the text will only be invisible if that symbol is currently
part of `buffer-invisibility-spec' (and that is used by
`dired-hide-details-mode').

buffer-invisibility-spec is a variable defined in ‘C source code’.
Its value is (t)
Local in buffer lisp; global value is t

  Automatically becomes buffer-local when set.

Documentation:
Invisibility spec of this buffer.
The default is t, which means that text is invisible if it has a non-nil
‘invisible’ property.
This variable can also be a list.  The list can have two kinds of elements:
‘ATOM’ and ‘(ATOM . ELLIPSIS)’.  A text character is invisible if its
‘invisible’ property is ‘ATOM’, or has an ‘invisible’ property that is a
list
that contains ‘ATOM’.
If the ‘(ATOM . ELLIPSIS)’ form is used, and ‘ELLIPSIS’ is non-nil, an
ellipsis will be displayed after the invisible characters.
Setting this variable is very fast, much faster than scanning all the text
in
the buffer looking for properties to change.