Render Appearance Image Fade

Example scenario:

I have an image I specify, then I select a color, but when I render the image never represents the color I specify.

For some material render appearances, such as the Default > Generic, there is an option to specify an Image and a Color:

 

Notice the setting below, for Image Fade.  Image fade controls the composite between the base color and the diffuse image.

Keep in mind, at 100 % the image file will completely override the color.  At 0 % the color will completely override the image file.  For example:

 

You can strike a balance between a color and image file using these settings as needed: