Camera linked to a null => null's scale gets inverted?

I have never thought about scaling something that has a camera as a child, so I tested it and it behaves like anything else. When you downscale, the camera, and thus the FOV shrinks, and when you upscale, the FOV scales with the camera. The ratio is maintained. 

To mitigate, either change the zoom of the camera, which is found under the camera options of the layer, or move the camera in z-space.

Try not to scale when you have a camera as a child, you'll get undesireable results, as you have found out!

You probably have not gone through any of the tutorials Adobe offers in the Learn section of the AE Home screen or the AE product page. Here's what you will find: Basic AE

Do that. Spend a couple of hours and you will have a much better idea of what is going on.

Here is your basic mistake. A camera does not have a scale property. It's not there. If you parent a camera to a null and you scale the null it will basically screw everything up. You move the null to move the camera. Simple as that. Leave the scale alone. Moving the camera is different than a zoom. In a zoom, the focal length of the camera changes so the framing changes.  Perspective doesn't change, that is controlled by camera position in real life, in AE, and in every other app that I have ever used that has a normal camera.

If you want to actually zoom, select the camera, press "aa" to reveal all of the camera's editable properties and set some keyframes for zoom.  You should make a mental note. Your eye cannot zoom so a zoom is most often an unnatural kind of movement that is usually not as effective as a moving camera when you are telling a story. Almost every feature film and television drama has no zoom shots in them. Movement in the scene is almost always a camera move. If the director throws in a zoom it is for an unnatural effect shot. Use animated zooms with caution. It is almost always best to try a camera move first.