While investigating ways to get the Cairo graphics API to draw a single-pixel line, I found this explanation in the FAQ. It explains why often a single-pixel line gets drawn as a half-intensity line two pixels wide.
The reason that cairo does it this way is so that fills align nicely, at the cost that some strokes do not. It is not possible to set up sample locations in a way so that both fills and strokes with integer coordinates work nicely, so one had to be preferred over the other. One argument in favor of preferring fills is that all fills with integer coordinates align nicely this way. The best that can be done with strokes is to make all even-integer-width strokes align nicely (as they do in cairo) or to make odd-integer-width strokes align (which would then break the fill alignment).
After reading this explanation, I still don't understand why this is a problem with graphics generally. What do they mean by odd-integer-width strokes breaking the fill alignment? Why is it such a problem to have both fill and stroke aligned to whole pixels?
I guess I don't really understand why or how the stroke width affects the fill at all.