OK, I think I figured it out. The paint tool seems to have this problem with terrains that a) are smaller than the default 64x64 cells, b) have non-square "resolutions" (i.e. rectangle), and c) have dimensions that are not powers of 2. I was having this problem in particular on my 50x30 terrain, but my old 64x64 never had it. Such things would be nice to know before I created most of the level on a faulty terrain. :-/
I also noticed something strange: I don't seem to be able to create terrains of sizes slightly larger than 64x64, e.g. 90x70: the resulting terrains always default to 64x64. I can, however, create a 300x300 terrain, which is weird.