I really think it comes down to laziness. Is it sometimes inconvenient to stop what you're doing and take your baby to the restroom for a diaper change? YUP, it sure is, but it's a part of being a parent - your life is no longer yours to do what you want when you want.
I can't count the number of times our DD needed a diaper change while we were at Disney and we had to stop what we were doing or where we were going to change her. It honestly didn't bother us one bit, but I'm sure other people find it absolutely inconvenient - why they had kids, I'll never know.
The only other public place we have ever changed DD is on the backseat of our car. We always use a disposable changing pad, even in our own car and we're sure to use wipes or antibacterial gel on our hands as soon as we're done. We change DD in a restroom, use a wipe on our hands, bring DD out to the other person and then go back in to wash our hands.
It's a process and it takes a few extra minutes, but it's safe for DD, for us and for people around us.