So I figured I'd give something a try. I used a 1-inch angled brush (out of this pack) and white paint. When we bought samples to decide colors of our rooms, we got two kinds of white samples as well (and they're "flat" not "semi-gloss). It's not the same color as the ceiling, but for the little that I used in the creases/corners it was close enough.
I dampened the 1" brush with water a little bit first. Then I dipped into the paint just the tiniest bit, wiped both sides of it on the edges of the paint container to let the excess paint drip off, and very carefully brushed the corner between the wall and ceiling. It's very delicate work because you don't want the bristles to bend or any paint to squeeze or drip out to make a thicker line than you need. I had to wipe off what I had just brushed on a few times because the line was thicker than it needed to be.
Here are some before and after pictures. The line isn't perfect and some spots will need a second coat of white (we are going to paint our ceiling anyway), but it looks a lot better than it did before and it only took a few minutes. And when you're not up close to it (which nobody will be since it's on the ceiling!) it actually doesn't look that bad at all.
Not too shabby, huh? Photos #7 & #8 are actually on a flat 2x4 door frame which we are also going to [primer &] paint so I'm not too worried about the big red line.
Maybe this is what those painters meant when they said "use a good angled brush and you'll never need tape again!" But I still think I'd mess it up. They'd want you to use a bigger brush to "cut in" and I would definitely hit the side I didn't want to paint. It was fairly easy with the tiny brush to just stay right in the crease, but cutting in and "feathering" with a large brush and more paint would be more difficult. Maybe I'll try in the bedroom...or maybe I won't!