A CBC is just a complete blood count--they enumerate the number of red/white blood cells, get hemoglobin levels, etc. This test, and a chemistry panel, are the most common blood tests ordered. I can't imagine Alan hasn't had one recently--probably more than one.

Does Dr. Fred, or Dr. Goldfarb (more likely the former) have a recent one on file?

Hospital may want to their own anyway--they're funny that way; think that their testing is more accurate than something that comes through a doc's office or outside lab center.