How to reproduce:
1. Open scene "Repro" in the provided project
2. Select the "Our Hero" GameObject in the Hierarchy view
3. Open Animator window
4. Observe that "Idle" is the default state, and that "Scale Animation" is also present, but no states transition to it
5. Open the Animation window
6. Observe that the "Idle" state does not animate any properties
7. Select the "Scale Animation" animation from the dropdown
8. Observe that the "Scale Animation" animates the Transform.scale property (specifically, the x and y axes)
9. Enter play mode
10. While in the "Idle" state (default), attempt to modify the scale (any axis) of the "Our Hero" object in the inspector
11. Note that the scale property does not change from its default of 1
Note: Same happens if other properties are animated in "Scale Animation"

By Design: As soon as some properties are driven by a State in the Controller, it is always controlled by the Animator. One can modify the values in LateUpdate();, but he/she has to modify them at each frame.