3-3 invasion into 4-4,6-4

Question

In josekipedia, they state that this exchange is a mistake

See http://www.josekipedia.com/#path:pdttpfqcpcqdqepbobrbpaqaqb for the full sequence they argue with.

But, I think that their argument is wrong! Why would white not follow making this shape, which is alive?

It is true that there are perhaps better possibilities for white's second move (in terms of points, not life & death), but the followup of the "mistake" and argument they present doesn't seem right for the above reason. Or did I miss something?

EDIT: actually, this shape works in the following joseki: http://josekipedia.com/#path:qettodqcpcqdperb

Answer 1

Maybe I'm missing something, but I don't think that shape is alive.

$$B 
$$ ----------------------------
$$ | . . . . . . . . . . . . . .
$$ | . O 7 1 . . . . . . . . . .
$$ | 4 . O X . . . . . . . . . .
$$ | . 5 O X . . . . . , . . . .
$$ | 6 2 X . . . . . . . . . . .
$$ | . 3 . X . . . . . . . . . .
$$ | . . . . . . . . . . . . . .
$$ | . . . . . . . . . . . . . .

7 is atari, so White loses the eye in the corner.

$$B 
$$ ----------------------------
$$ | . . . . . . . . . . . . . .
$$ | . O . 1 . . . . . . . . . .
$$ | 5 . O X . . . . . . . . . .
$$ | . 4 O X . . . . . , . . . .
$$ | . 2 X . . . . . . . . . . .
$$ | . 3 . X . . . . . . . . . .
$$ | . . . . . . . . . . . . . .
$$ | . . . . . . . . . . . . . .

This is dead, too.

$$B 
$$ ----------------------------
$$ | . 5 . . . . . . . . . . . .
$$ | 4 O . 1 . . . . . . . . . .
$$ | 3 . O X . . . . . . . . . .
$$ | . 2 O X . . . . . , . . . .
$$ | . . X . . . . . . . . . . .
$$ | . . . X . . . . . . . . . .
$$ | . . . . . . . . . . . . . .
$$ | . . . . . . . . . . . . . .

And again.

Update: Turns out I didn't show the trickiest variation. When White plays 4, 5 is hard to find, but it's often a tesuji in this kind of shape.

$$B 
$$ ----------------------------
$$ | . . . . . . . . . . . . . .
$$ | . O . 1 . . . . . . . . . .
$$ | . . O X . . . . . . . . . .
$$ | 4 . O X . . . . . , . . . .
$$ | . 2 X . . . . . . . . . . .
$$ | 5 3 . X . . . . . . . . . .
$$ | . . . . . . . . . . . . . .
$$ | . . . . . . . . . . . . . .

I think White is still dead. If he goes this way, 4 is the tesuji:

$$W
$$ ----------------------------
$$ | . 3 2 . . . . . . . . . . .
$$ | 4 O 1 X . . . . . . . . . .
$$ | 5 . O X . . . . . . . . . .
$$ | O 6 O X . . . . . , . . . .
$$ | . O X . . . . . . . . . . .
$$ | X X . X . . . . . . . . . .
$$ | . . . . . . . . . . . . . .
$$ | . . . . . . . . . . . . . .

Here he gets a false eye:

$$W
$$ ----------------------------
$$ | . 4 . . . . . . . . . . . .
$$ | 1 O . X . . . . . . . . . .
$$ | . . O X . . . . . . . . . .
$$ | O 3 O X . . . . . , . . . .
$$ | 2 O X . . . . . . . . . . .
$$ | X X . X . . . . . . . . . .
$$ | . . . . . . . . . . . . . .
$$ | . . . . . . . . . . . . . .

This way, the throw in still destroys the lower eye.

$$W
$$ ----------------------------
$$ | . 3 . . . . . . . . . . . .
$$ | . O 2 X . . . . . . . . . .
$$ | 1 . O X . . . . . . . . . .
$$ | O 4 O X . . . . . , . . . .
$$ | . O X . . . . . . . . . . .
$$ | X X . X . . . . . . . . . .
$$ | . . . . . . . . . . . . . .
$$ | . . . . . . . . . . . . . .

Answer 2

White hanes at S15, and when Black counter hanes at S14, White plays the key move, Q18. After two hane and connection moves, White lives with T16, ending the sequence.

Black should have haned at S 18 instead of playing 1 (R15), and then connected at R18.That forces White to crawl along the second line to S14, just to live. Black plays R13, and has White running along the "line of defeat."

The corner sequence is "double sente" for either Black or White, and more to the point, relates to the life or death of White.