Hitfilm Parenting behavior discussion
This video shows the behaviour in HF3Express, but you can load the project file at the link below into HF3P and HF4P and get the same result.
Download Project File
Background: I'd made one of the planes 3D, then deleted the camera, which reset the plane back to 2D, but it apparently thought it was still 3D and responded like this: (that was a Red Herring, read later posts)
[mod edit: update the subject based on the subsequent disussion]