In FDI, an Author user was unable to save a workbook containing an iframe when Allow Scripts was enabled. The following error was displayed:
"User does not have authorization to save."
Although the UI allowed the user to toggle Allow Scripts to On after a few attempts, the workbook could not be saved. When Allow Scripts was set to Off, the same Author user was able to save the workbook successfully.
In standalone OAC, there is a fine grained permission called "Allow Advanced Options in Iframe Visualizations." By default, this permission is granted only to the BIServiceAdministrator role. The same restriction applies to FDI behind the scenes, meaning that only administrator users are allowed to save iframe content with scripts enabled by design.
To confirm this behavior, I granted the "Allow Advanced Options in Iframe Visualizations" permission to the Author user's application role in OAC. After granting the permission, the user was able to save the workbook successfully with Allow Scripts set to On.
However, in FDI, this fine-grained permission is not exposed, so there is currently no option to grant it to an Author user or application role.