Hey @dd,
To make sure that folks cannot edit their information, all you have to do is this:
1. Go to Events → Settings → Tickets in your wp-admin
2. Scroll down to the “Login requirements” section
3. Make sure both options are NOT checked, as shown in this screenshot (click for a larger-sized image):

People will only be able to edit their ticket info if both options are checked, so just leave these unchecked and they can’t edit the tickets! 😀
Please let me know if this helps, and if there are any other issues or questions I can try to help with.
— George