This is silly, in my case, but it turns out I WAS doing everything right. I even saw someone say he had to close and restart iTunes for it to work. I did it a couple of times but no go. Until finally, I gave up closed iTunes, decided to open it back up to sync my phone just in case, then I saw this:
Please notice the blue-highlighted bell on top. That is the Music Library on your computer and its 'subfolders' for music, videos, tones, etc...
I was trying to drag the m4r or even the m4a and mp3 into my Phone's Tones 'subfolder' which is what is visible on the left hand pane of iTunes when you open it and your phone is connected to the computer.
So it turns out I had successfully imported it 2x already and then a 3rd time.