Personally, I'd probably take the learning lesson on this one and avoid turning it into a bigger issue than it needs to be.
From your description, it sounds like this customer is very detail-oriented and wants a high level of control over the process. When I see that early on, I usually assume anything not documented may come back up later.
I'd accommodate the request if it's reasonable, finish the project strong, and then update the contract/process going forward. Sometimes the cheapest lesson is the one that helps you avoid the same situation on future jobs.
One thing I've noticed is that customers who get hung up on details early are often telling you exactly how much communication and documentation they'll need throughout the project.
