The fossil record is the claim not the evidence

[Angrboda]

You are being too charitable. There is another feature played out in the fossil record that was predicted by evolution before it was truly discovered. The simpler organisms procede the more complex ones. Obviously there are reversion's and simple organism that survive very well, such as horseshoe crabs, but this is the order in the sediments (you do not need to even under stand the geologic colomn or its age to understand that bottom sediments are older.)
Invertabates
Fish
Amphibians
Reptiles
Mammals.

When a theory predicts the behavior of a natural phenomenon, that phenomenon is evidence for that theory. Much like the law of attraction is phenomenon that is predicted by the theory of gravity by newton.

I didn't say it wasn't evidence in support of the hypothesis of evolution, only that it doesn't rule out other interpretations by itself. And note that you brought in additional lines of evidence in order to count "a hit," but didn't subtract a hit for the paucity of the fossil record, and its less than stellar testimony to transitional forms. Being skeptical means you count both the hits and the misses, and weigh all hypotheses on the same scale. Arguably, on the fossil record alone, ignoring shared assumptions, evolution still wins, but it's no longer a slam dunk and therefore becomes a claim in need of additional evidence.