They don't. The updates are pulled by your router, not pushed from their server. So, it doesn't give them any more access than they would have if you were to download and flash a firmware manually. It's the same firmware image after all, where you already put your trust in them regarding what it contains.I don't agree with auto-updates in any way, shape, or form on a router because that means Asus (or anyone else) has deep access to our network/systems.
A more valid reason to dislike automatic update would be because you want to wait to ensure that no major issue is found by other users, and also to have the option of running an older version if the newer one has problems. Or because you don't want your router to blindly reboot itself while in the middle of downloading a nighttime 100 GB backup. Those are legitimate reasons to want to retain full control as to when updates are deployed.