Hi @Elliot,
After more testing, I think this bug is a «false positive». It seems the problem was due to files being added to the translated post before WPML Media was activated. As a result, the Media modal tries to get the data for the file in the original langauge, which it doesn’t have access to after WPML Media is installed. I created a new translation, and the problem wasn’t replicated.
This particular project is huge, and I have editors adding content while I’m developing, thus the blooper. Cancel red alert.