Is it possible to transfer E-O157 from simply touching something with contaminated hands? Today I went to eat at a local hamburger chain with my family. It was the type of restaurant where you can clearly see the workers making and prepping the food. While observing them make our food, I witnessed the cook take out the raw hamburger patties (with a gloved hand), put them on the grill, grab the buns and cut them in half, line up the plates, place the toppings on the bun, then continue cooking the hamburger, all with the same gloves. Being a little paranoid about my children getting unnecessarily sick, I immediately informed the manager and requested new buns and toppings with fresh gloves. The manager didn't seem to think a whole lot about it, but still granted my request, but I definitely had to spend the rest of the stay with some death stares from the staff. After leaving, I started to wonder if I was being a little unreasonable since I have been seeing this practice more and more at different restaurants and fast-food joints.

I have read ALOT of questions on this site about the risks of cross contamination but most of it involves best practices and food being cooked together, like this, and this, and this. 
Based on all my reading, I already know this is not good practice, but what I am curious about is if any of the bad stuff, like E-O157 can actually be transferred to the buns and toppings in this manner. 

Am I overreacting about the risks associated with this practice, or are the risks relatively low? More specifically, is it even possible to transfer enough of the bad stuff to make someone sick by using the above practices?
It's not unusual for a line cook to handle several things at once, but I can certainly understand your concerns. It would be preferable if the cook could pick up the burger with a seperate utensil, dedicated to the burgers. With someone else assembling the plate (bun, side dish and "fixin's").

The issue(s) with E-O157, as I understand them, are primarily a result of contamination during production. In NC, an establishment that grinds their own meat is allowed to serve the food product at any temp the consumer requests (even to the point of Steak TarTare - yum!). The reason is simply that they are in a more controlled environment and the risks are significantly lowered/eliminated. Businesses that have their ground beef processed off-site are limited to cooking it well enough to kill the bacteria. Typically, "well done".

Cross-contamination is a "thing", but a restaurant employee is more likely to think of it as: don't put the potato salad spoon into the spaghetti sauce, or don't stick the meat thermometer into the soup pot. Picking up lettuce and then reaching for a slice of tomato... is generally "ok". I do agree that it would be unappealing to see what you described. 

The US Dept of Agriculture/USDA provides much more information on their website.