I have a double facepalm for you:
- I tried to generate the outputs (for the first time) - it showed "Validation failed" (no info where it failed).
- so I fixed the DRC errors (left them before, because they were not important),
- still Validation failed,
- I tried to fix all ERC errors too (there weren't any, so I fixed all warnings at least),
- still Validation failed,
- then I tried to determine which output fails, so I disabled everything except for the BOM,
- it generated the Gerbers succecssfully - even the disabled ones!