False, the turnips you avoid during the match are thrown for spacing purposes, most of the time you get hit by peach because you avoided some turnip.
You gotta get around stitchfaces differently, because Peach actually wants to hit you with it.
The "Z-catching it in midair" thing is also overrated, because she will put you into a really bad situation before throwing it.
A good example of that is Armada vs Mango at G2:
http://www.youtube.com/watch?v=CQ9c-2lAld4
At 14:05, we can see that armada doesn't directly throws the stitchface to Mango's face, he lands a fair before. That way, Mango won't be able to avoid the turnip because of the stun. And even if Mango does dodge it by using his getup attack, it opens a window for Armada to land a dash attack, which cost Mango his stock (because using the get up attack was the
only way to dodge the stitchface).
The infamous stitchface combo works that way, Armada waited to land a fair before throwing his turnip.
So, to avoid getting hit by a stitchface, remember those things:
-Peach will rarely just throw it at you, she'll try to combo you into the turnip.
-She
has to stay in float, since she can't use her ground moves and keep her stitchface.
-The best way for Peach to hit you straightly with the turnip (if she tries to), is to wait for you to be above her.
Therefore, I think the best way to beat Peach's stitchface is to camp the crap out of her: her options will be super limited, because she won't be able to stitchface you from a long distance (especially on FD/Dreamland/PS) and she can't outcamp you without letting her precious turnip go.
There might be other ways to get around it, but I think camping is the best one.
I'm too tired to re-read carefully my post, so pardon my bad english.