I have a feeling that I got lucky. There's another setting under "Keyboard" > "Accessibility", at the bottom, called "Full Keyboard Access". Mine is set to "All controls". I have a feeling yours is set to "Text boxes and lists only", which may be the default.

So I am kinda proving your point here :)

(The non-discoverable way is to press Ctrl-Fn-F7; it's non-discoverable because the only place these instructions are shown is the Keyboard -> Shortcuts tab, but you can't get to that tab without a mouse.)

Very close Apple. Just a little more polish for your next update.

Then when I go to the panel, I tab and it only highlights the left-side of the portion. Confused me at first but after mashing some keys I found that you need to press up/down on the left page to select the "mouse portion" THEN tab again and it will go "into" the place with the mouse keys. Here's a gif http://imgur.com/a/SedKz.

Edit: See nearby replies -- the reason you were able to do this is that you had previously changed a default setting which has no obvious way of being changed without a mouse.