Just caught an episode of "The Secret Life of...." on the Food Network that featured delicatessens. I don't think it was a new show but the relevant thing was that the final featured deli was Langer's. Norm Langer proceeded to explain the whole pastrami thing at length and made it very clear that ALL their pastrami is hand-cut (or at least that's what he said, though I've read here of people who've seen it cut by machine as well.)
His explanation was that their pastrami needs to be hand cut because it so tender due to extra steaming and requires the manual touch of a counter-person to trim fat and continually cut against the grain by turning the meat as the grain changes during cutting.
I can hardly wait to see what responses this brings, but there it was........ a real Langer, in person, saying it's all hand-cut.