Oops. The sanity check was to see that circles are proper circles for all screen modes despite various screen aspect ratios.
Sure enough, the circles are proper circles regardless of screen aspect ratio.
Which means the CIRCLE command does some fancy math to make sure that circles don't turn into ovals when screen aspect ratios are not 1 to 1 (i.e. 1 pixel wide to 1 pixel tall, as opposed to a 2.4 pixels wide to 1 pixel tall, for example.)
So the fancy and super-speedy subroutine somebody gave me to create filled-in circles via creation of triangles, fine when in a 1:1 screen ratio, but creates ovals otherwise.
Anyway, that's the details of what I was investigating, just in case you also geek out on this kind of stuff.