Oh, I've got it! I know what I've done differently!
In Tools > Options > OOoDraw > Grid, I set the resolution to 1
point. Then at some magnifications, the grid appears to be lines,
not dots (because they are so close together, I assume). This
works also for other combinations of resolution and
magnification, including 0.1 cm and 0.2 cm. I must have just
accidentally stumbled on a combination that made lines when I was
doing this earlier.
This may be an artifact of my high-resolution monitor. I'm
booting up another machine now to check this there.
Cheers, Jean