The sky light provides an Ambient Fill light as opposed to an actual light source. Even if you have a completely enclosed area, the sky light is going to fill that space. This is more clearly seen when you toggle is lower hemisphere black on or off.
When you add a sky light you are adding a fill light for the entire scene. I ran a test with a cube made from six cubes. The walls are fairly thick. I added only a sky light to the scene and set this to static. I then baked lighting at production lighting quality. I am able to see a slight illumination in my scene. This is to be expected. I then added a static point light reduced the attenuation so that I would also see the affects of the static sky light. Again, light was behaving as I would expect.
The fill lighting of a sky light is based off of the environment is reflecting. IE if you have no BP_Skysphere or some influence for the sky light in your scene to reflect then your fill light will be black. I will post three screenshots below to demonstrate.
This first screenshot is with no Sky_Sphere. The skylight has literally nothing to influence the scene with. The environment is completely black.
This screenshot is with no source light and a Sky_Sphere within the scene. The sky sphere looks like evening.
You will notice the change in color and illumination of the inside of this box. These are both captured after lighting has been built.
The last screenshot is made with a directional light influencing the time of day of the sky light. All lights are still static.
Note the illumination and influence of the sky light but also note the color change which is influenced by the color of the sky sphere. What happens when you change this to stationary is that you are updating your lighting in real time and using light bounces as opposed to baking the lighting where the engine calls on the lightmass build. Therefore, you will see the update in the viewport. This explains why you are seeing the influence more defined when you switch from static lighting.