Tile can be painted, yes, but you need to prepare the surface area beforehand with a primer. And not just any primer, but one that's really adhesive - otherwise the paint will scrape off. Luckily, Sherwin-Williams has a primer designed specifically for painting tile. That said, your hunch is spot-on. Painting wall tile is one thing, but painting a floor is another. Don't try to paint the tile you'll walk on. Even with the best adhesive, that paint will just scrape off. A simpler solution is to place new flooring on top of it. I recommend laminate. Laminate floats on top of existing floors and is easy to install, requiring no adhesive. Or you can put new tile over the old, ugly tile, which is fairly typical, and shouldn't be a problem unless the old tile is crumbling. Good luck! We'd love to hear how this goes. Post before and after pics to Money Pit's Facebook page.