Can someone confirm if this is normal behavior? It appears the noise texture by default is "squeezed" in the z axis. Below I am showing it as default and with scale up by 0.5 applied to lengthen in the z axis.
Texture coordinates matters
No, by default the noise texture is isotropic. Here's a picture of it covering the default cube:
You are probably experiencing that "strange" behaviour becaues you are feeding the vector socket of the texture with a non-uniform vector fields.
As said in the manual, Generated texture:
... [automatically-generate] coordinates from the vertex positions of the mesh without deformation, keeping them sticking to the surface under animation. Range from 0.0 to 1. 0 over the bounding box of the undeformed mesh.
This means that if your object has a non-uniform bounding box (even a loose vertice counts), you'll get different density of the vector field in the 3d space to be able to guarantee the same range. A tall object will show a stretched texture upon the z-axis, while in a short (as in your case) will look squeezed.
See in this image sequance how altering the x-size of the object by modifying its mesh (e.g. moving some vertices) leads to a stretch of the texture on that axis.
If you want to keep the texture's size indipendent from the object's bounding box you should use Object Texture coordinates, maybe targeting an Empty if you want to keep the size consistent across multiple object (Object's Texture coordinates is object's transformations dipendent).