No, the webcam proctor cannot access your computer files without your knowledge.
With permission from the test taker, proctors have the ability to view the screen and move the mouse and keyboard as if he or she were sitting next to the test taker. Once the test starts, the proctor will monitor everything but can no longer move the test taker's mouse and keyboard. During the entire process, a chat box is running on the test taker’s computer, and they can see what permissions the proctor currently has at any time. The entire chat session log is saved, and there is a permanent record of what actions the proctor took while accessing the test taker's computer.