> The impression I certainly got was that his approach is to theorize about something, then design experiments to test out his theory. As opposed to running a bunch of experiments and then figuring out a theory that would explain the collected data.
There's nothing wrong with this, as you've written it. (There might be a problem with his implementation.) All else being equal, I trust a theory which has made ten accurate predictions over a theory which merely explains ten previous observations.
If one person develops a theory and makes ten predictions which turn out to be true; and if a second person observes the same ten things, and then develops a theory without knowing the first; then I consider this stronger evidence in favor of the first theory than of the second. (The second might e.g. be more elegant, in which case I might prefer it anyway.)
This is true whatever the observations are. If they're unsurprising, then we already had a good theory, in which case I question the need for the two new ones, but that applies to both equally.
It may be that Kurzweil is falling into the trap of misinterpreting his results to fit his theory, but that can be done just as well when you try to base a theory off existing data. On the other hand, the Texas sharpshooter fallacy can only happen if you collect data before coming up with your theory.
There's nothing wrong with this, as you've written it. (There might be a problem with his implementation.) All else being equal, I trust a theory which has made ten accurate predictions over a theory which merely explains ten previous observations.