Q: ...I made three simple bitmaps in Animator Pro; each was just one solid color. In 3DS4 I made textures from them, then three more materials using the same RGB values as the bitmaps for the Ambient/Diffuse colors. They don't match the mapped textures at all, either in the sample windows in the Materials Editor, or when assigned to spheres in 3D Editor and then rendered. Why is this?

A: I tested it at home yesterday and could not reproduce your problem. (at least not with my first try...)

I created a GIF in Animator 1.0 with pure RED (63,0,0) and dark red (32,0,0)
I created a basic material with pure red (255,0,0) in Ambient and Diffuse slots and one with 128,0,0.
I created a 3-segmented cylinder and a L-sphere. Assigned the basic material to the whole object and the mapped material (with face mapping) to the middle parts of both objects. There was ALMOST NO DIFFERENCE!

Picture 1 shows both materials on both objects:

Here is a picture of the same scene with Mapping OFF in order to show what it looks like without mapping:

Picture 3 shows the same scene with the second material combination (dark red):

Picture 4 shows what happens when the GAMMA CORRECTION for INPUT FILES (1.0) is not matching the MONITOR/FRAMEBUFFER GAMMA and OUTPUT GAMMA (1.8):

So please first make sure your GAMMA SETTINGS have the correct values...

Addition:

Note that these settings are system dependent! Read the manuals for more info on Gamma correction.