I just purchased the white Xbox One S and an additional controller. I received the console 48 hours ago and BOTH controllers have this issue. The button does not stick all the time, it sticks when pressed slightly off center. I have owned several Xbox 360 controllers as well as many controllers from other companies, and none of them have had this problem.
It's clearly a flaw with the controller's design, as both controllers have the issue and and I can easily make the issue repeat itself. Jason, did you ever get resolution on this?