Operating system: Windows-10-10.0.18362-SP0 64 Bits
Graphics card: GeForce RTX 2060/PCIe/SSE2 NVIDIA Corporation 4.5.0 NVIDIA 442.92
Broken: version: 2.90 (sub 3), branch: master, commit date: 2020-05-22 20:59, hash: rB86fa8dc7f73a
Worked: it has never worked properly.
Short description of error
As per design this should result in rotation all object based on the local transforms of the selected object, but instead it tries to transform each object to its own local transform which is to be the result for an other combination (local transform orientations + individual origins transform pivot point.)
Exact steps for others to reproduce the error
Create a new scene,
Duplicate select the 3 objects in the scene (camera, cube and lamp)
Select the aforementioned combination, local tranforms and active element pivot
Rotate your objects in any particular axis (in trackball seems to work correctly?, but that defeats the purpose of using local axis)
Now try the same but with 3 bones, the results are even stranger.
Combining transform orientations and pivots in blender is an essential part of the workflow and very powerful, some of the combinations have been overlooked, like when using "local transform orientations" but in "active element pivot"