The PCB manufacturer contacted me today to explain. She told me that 100% will work, but up to 5% may have aesthetic flaws. This was apparently by accident, and she will be replacing our boards with scratches / paint blobs. I'm guessing they assume most buyers are installing these into complete products and that end consumers won't really see the PCB so the aesthetic flaws don't matter.
Obviously, we'll be removing all of the PCBs with aesthetic issues from our inventory, so no one should have to worry about this again.
Thanks for everyone's patience as we tackle these new product types!