FWIW, Coda Support replied to my Intercom message and directed me to this:
Now… to find out how I disable that…
Update:
The fix to disable was to change the advanced setting for “Anyone with a link” to “Can View”, or something more restrictive than “Can Edit”. It’s the combination of having the link, and an open “Can Edit” permission that triggers the user being asked if they want to edit anonymously.