This response is four years late, but I want to expand on what is written here in case anyone searches this exact question.
For some reason, when you change your control scheme such that C-stick inputs perform special attacks, Brawl seems to press a jump input while also performing a special move (I have noticed that this sometimes leads to unwanted jumps if you buffer special attacks using the C-stick, but I haven't found the conditions which make this consistent.) This means that if you attempt to do Smash4-style bidou (using the methods described in
this video), you just input a jump instead of turning around.
You can still get Bidou, however, if you hold both special and jump while inputting the C-stick. For example, I can set Right Trigger to Special Attack and the Z-Button to Jump, and hold both buttons down before flicking the C-stick left to turn my character around.
Can you use this to perform perfect-pivots in Brawl? Unfortunately, no, you can't. (By the way, you
can perfect-pivot in Brawl, although the characters don't slide afterwards like they do in Smash4 so it's much more situational.) If you dash right while holding both Special and Jump and immediately flick the C-stick left, your characters continues running right as if you didn't input anything at all. So you have perfect-pivot in Brawl the hard way.
The only known use for this technique is to spin turn your character around while walking forward (in
this thread, it is referred to by "pivot walking"). For some reason, Brawl characters walk faster when they turn around, so by briefly inputting a direction behind you while walking you actually increase the speed of your walk.
You could also use this technique to approach with shields with your back behind towards to the opponent (since walking forward in shield is a very good option in Brawl). You would do this by walking forward, using Bidou to turn around, and then immediately pressing shield. This would be useful if you play a character with very good out-of-shield options behind them (say, Yoshi's Bair, or Fox's Utilt).
Of course, you don't need to change your C-stick to jump to do this. As was known for years before Smash4 came out, you can pivot walk with the C-stick set to Smash if you hold down the A-button (either by clawing or by setting a trigger to Attack) while flicking the C-stick up and to the right/left. Pushing up-right/up-left is important; of you push the C-stick all the way to the right or left, you just input a Smash attack, and if you push the C-stick close to straight up, you input a forward dash (?). So you have to point precisely to the top-right/top-left corner of the C-stick to input a turnaround.
You can also do this with the C-stick set to tilt by holding the A-button and jump button (setting the C-stick to tilt also inputs jumps just like setting it to special).
