Windows 10, NVIDIA GeForce GTX 960 (btw it doesn't matter)
2.76b, or any other versions (as far as I know)
Short description of error
This problem occurs when importing animation using fbx to UE4 or to Maya. I have already talked to the UE4 devs. They managed to reproduce the bug, and said that the problem is on Blender's side. So that's why I ask for your help.
Shortest way to achieve the problem: I have two bones: a child and a parent. The child bone doesn't inherit the scale and the rotation of the parent. I only animate the parent bone.
If the animation for the parent bone only contains rotation and move then the child bone acts as it should in UE4. (It doesn't rotate) If the animation for the parent bone contains rotation, move and scale then the child bone will also be rotated to the mirrored direction. It still doesn't inherit the scale transform from the parent, but it is rotated. My guess is that it does the counter rotation twice (or I am not sure how it is translated if it doesn't inherit the parents rotation). The weird thing is, that the problem is with the child's rotation, however it only happens if I scale the parent.
Exact steps for others to reproduce the error
Link for the original bug report in UE4 forum (with blend files, fbx and a video where I reproduce the issue)