Just did it. Cmd+Space to bring up Spotlight. Type "Syste" and hit [enter]. The search box in the top-right corner should be active. [Tab] to it if it's not. Type in "Mouse" and arrow down to "Make mouse and trackpad easier to use". Hit [enter]. Hit [Tab] twice to move focus to "Enable Mouse Keys". Spacebar.

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 :)