I wasn't sure if there was a name for the technique, but I was corrected, (Thank you, DMGregory) and a common name for the technique would be having a "specular mask", where a colour channel of a texture "masks" or controls the intensity of the specular reflection. This is demonstrated below in this code which is actually an excerpt from the code of the shader you show in your screenshots.
void surf (Input IN, inout SurfaceOutput o) {
fixed4 tex = tex2D(_MainTex, IN.uv_MainTex);
fixed4 c = tex * _Color;
o.Albedo = c.rgb;
fixed4 reflcol = texCUBE (_Cube, IN.worldRefl);
reflcol *= tex.a;
o.Emission = reflcol.rgb * _ReflectColor.rgb;
o.Alpha = reflcol.a * _ReflectColor.a;
}
The part most relevant to your question are the lines reflcol *= tex.a;
and o.Emission = reflcol.rgb * _ReflectColor.rgb;
where, first, the alpha channel of your base texture is factored into the colour of the reflective cubemap texture and then that colour is made to be the Emission
term of the output. The Unity wiki says that the Emission term shows up even if the surface is in absolute darkness, like it might be if it were in shadow. This also explains why the reflection showed up even if the texture was nearly completely black.
So, you could say that the shininess of the surface depends on where the base texture is or isn't transparent, and if you opened up the texture for the tire in an image editor, you'd see that some sections like the tire treads would be mostly transparent.