The thread referred to discusses cycles in a world WITHOUT pass-for-ko (and with the principle of "two-eye-formations" instead of "uncapturable"). Thus, the double-ko cycle with a length of 8 (including 4 "pass") would no longer be ENFORCED. Black would interrupt it with moves in the upper left corner, killing White's group there.
A remaining cycle for the position of L89's L&D Example 17 would be an OPTIONAL one -- in principle:
$$W :w3: pass
$$ -----------------------
$$ | X X X . O X 1 X O . O X . .
$$ | . O O O O X X O O O O X .
$$ | O O X X O X O 2 O X X X
$$ | . O X O X X X O O X .
$$ | O X X O X . X O X X .
$$ | X X X O X X O X X . .
$$ | . . X O O O O O . . .
$$ | . . X X . . . . . . .
$$ | . . . . . . . . . . .
$$ -----------------------
- Click Here To Show Diagram Code
[go]$$W :w3: pass
$$ -----------------------
$$ | X X X . O X 1 X O . O X . .
$$ | . O O O O X X O O O O X .
$$ | O O X X O X O 2 O X X X
$$ | . O X O X X X O O X .
$$ | O X X O X . X O X X .
$$ | X X X O X X O X X . .
$$ | . . X O O O O O . . .
$$ | . . X X . . . . . . .
$$ | . . . . . . . . . . .
$$ -----------------------[/go]
$$W :b6: pass
$$ -----------------------
$$ | X X X . O X O 4 O . O X . .
$$ | . O O O O X X O O O O X .
$$ | O O X X O X 5 X O X X X
$$ | . O X O X X X O O X .
$$ | O X X O X . X O X X .
$$ | X X X O X X O X X . .
$$ | . . X O O O O O . . .
$$ | . . X X . . . . . . .
$$ | . . . . . . . . . . .
$$ -----------------------
- Click Here To Show Diagram Code
[go]$$W :b6: pass
$$ -----------------------
$$ | X X X . O X O 4 O . O X . .
$$ | . O O O O X X O O O O X .
$$ | O O X X O X 5 X O X X X
$$ | . O X O X X X O O X .
$$ | O X X O X . X O X X .
$$ | X X X O X X O X X . .
$$ | . . X O O O O O . . .
$$ | . . X X . . . . . . .
$$ | . . . . . . . . . . .
$$ -----------------------[/go]
The last genuine move (i.e. NO "pass") of the cycle would be a WHITE one.
White (as well as Black) would be discouraged to START this nonsensical cycle that only lengthens the confirmation sequence.
In addition, this cycle is NOT ENFORCED, so Black would be free to use his

for an atari in the upper left corner, achieving the same result as with banning the last genuine move in that cycle.
++++++++++++++++++++++++++
Under J89 ...
$$W :w3: pass-for-ko
$$ -----------------------
$$ | X X X . O X 1 X O . O X . .
$$ | . O O O O X X O O O O X .
$$ | O O X X O X O 2 O X X X
$$ | . O X O X X X O O X .
$$ | O X X O X . X O X X .
$$ | X X X O X X O X X . .
$$ | . . X O O O O O . . .
$$ | . . X X . . . . . . .
$$ | . . . . . . . . . . .
$$ -----------------------
- Click Here To Show Diagram Code
[go]$$W :w3: pass-for-ko
$$ -----------------------
$$ | X X X . O X 1 X O . O X . .
$$ | . O O O O X X O O O O X .
$$ | O O X X O X O 2 O X X X
$$ | . O X O X X X O O X .
$$ | O X X O X . X O X X .
$$ | X X X O X X O X X . .
$$ | . . X O O O O O . . .
$$ | . . X X . . . . . . .
$$ | . . . . . . . . . . .
$$ -----------------------[/go]
$$W
$$ -----------------------
$$ | X X X . O X O M O . O X . .
$$ | 4 O O O O X X O O O O X .
$$ | O O X X O X T X O X X X
$$ | . O X O X X X O O X .
$$ | O X X O X . X O X X .
$$ | X X X O X X O X X . .
$$ | . . X O O O O O . . .
$$ | . . X X . . . . . . .
$$ | . . . . . . . . . . .
$$ -----------------------
- Click Here To Show Diagram Code
[go]$$W
$$ -----------------------
$$ | X X X . O X O M O . O X . .
$$ | 4 O O O O X X O O O O X .
$$ | O O X X O X T X O X X X
$$ | . O X O X X X O O X .
$$ | O X X O X . X O X X .
$$ | X X X O X X O X X . .
$$ | . . X O O O O O . . .
$$ | . . X X . . . . . . .
$$ | . . . . . . . . . . .
$$ -----------------------[/go]
... Black would also attack White's corner group, as White is hindered to recapture into any ko-shape, as long as NOT ALL ko-bans have been lifted. And we can be very sure that Black will NOT pass for "his" double-ko ko-shape.
++++++++++++++++++++++++++
Yes, there is a difference between cycles with a length of
4, 8, 12, ...
and with a length of
(2,) 6, 10, 14, ...
(Without any pass-for-ko ban, it's only the latter type that can cause problems.)
Cycles can become "problematic" during status confirmation ONLY if there is a double-ko involved.
J89's "original" (i.e. as of 1989, according to James Davies' translation) version of IMMEDIATELY enabling the recapture into any ko-shape, which ko-ban has been lifted, apparently was designed for single-ko shapes only.
The unwanted side-effect was making the 8-move double-ko cycle ENFORCED (with the SAME player starting each half of it), turning it into a means for creating chôsei for other groups under consideration. Thus, the intended result of several L&D Examples could not be reached within J89
(1989).
++++++++++++++++++++++++++
The apparently unwanted 6-move-cycle of J89's L&D Example 23 -- which is "sending three, returning two" -- includes one "pass" at its end; so it's the same player who plays the first, and the last, genuine move of that cycle.
Banning the last move of that cycle would resolve a problem that cannot be solved within the application of the legal text.
Under J89
(<= 2007) it would be sufficient to limit this kind of ban to cycles that have a "pass" at their end.
EDIT: As J89 has "uncapturable", it would of course have the same effect to ban the repetition of the first move of the cycle.