Ewwwwwwww. this topic keeps giving me nasty mental images.
First of all, I've always stood to wipe, and no you don't stand fully erect, *cough* with your back, you lean forward a little as you stand and you spread your cheeks... lol... and you wipe. It's easy and clean. No poo goes anywhere like some dude stated, thats what um, the toilet paper is for? And you certainly don't get up until you're done. That's the only way I could see poop dripping down.. getting up before you're finished..
If you sat down to wipe your arm would touch the seat/rim and potentially take a mistaken dip in the water... you'd have to wash your arm up to your elbow! Which I seriously doubt anyone does!
However I do pee while sitting down (only at home though), because I don't like pissing all over my toilet. It's not hygienic at all. Microblobs of it go all over the place but you can't see it. Your urine is NOT a stream, it's a spray, your eyes just can't see the tiny dots of urine fast enough, but you can if you had a slow-motion camera... how do I know this? thank Mythbusters.
Now that I know half of the worlds population go around with urine coated elbows... NO MORE ELBOW HUGS!