I agree to the extent that I do not think God falsifies data to make things look any particular way. But I would argue that the data does not, to me, look like evolution, by itself, produced the data.
The diagram below you will never see in a biology text. But as I understand it, it shows how the fossil record used to be drawn, how it is drawn now, and what the fossil record really looks like.
NOTE: You have to click on the image to see the whole thing!
Click on the above to see the third image, which is most important! Argh! Software...
The separations get increasingly severe as you go up the toxonomic tree. Certainly some skips can be explained by "it's hard to become a fossil." But Niles Eldredge stated, "We palaeontologists have said that the history of life supports [the story of gradual adaptive change] knowing all the while it does not. … When we do see the introduction of evolutionary novelty, it usually shows up with a bang, and often with no firm evidence that the fossils did not evolve elsewhere! Evolution cannot forever be going on somewhere else." There is something here that we do not know, that leaves us "scratching our heads" as George pointed out. Is that the fingerprints of God, or not? We cannot be sure either way.
You are focused on the genetic data, but I suspect the same is visible there.
You can argue, as Daniel points out, that the anomalies must have a naturalist explanation. But usually that is an a priori philosophical orientation. If one only looks at data that supports the theory, then one will conclude the theory is correct. The problem is not there, but where the data does not fit the theory.