Sort of. They look at the trial record. Naturally, that is a view of the evidence allowed, but also, if evidence was WRONGLY EXCLUDED, the trial result can be overturned. See also, e.g., bringing DNA evidence into old cases to exonerate convicted criminals.
One thing the federal judge and the federal courts will NOT be looking at in this case is whatever part of the records Greer destroyed when he received the subpoena for them. Don't believe me? That is what Sensenbrenner was so frosted about when Greer ignored the subpoenas and he said so last Friday in one of the interviews he gave. (Hannity's radio show, I believe, but could have been Fox.) WHY would he do this? What is he hiding? Call me a conspiracy nut or Sensenbrenner a liar, but this stinks to high heaven.