Given the blindingly obvious differences between the Cowl on the Bat-Corpse, the one Bruce was shot in, and the one Superman gave to Nightwing, it seems far more likely that the Bat- Corpse is from an alternate Universe - especially as throughout Final Crisis characters such as Kamandi, Sonny Sumo and Nazi Supergirl were gravitating towards Earth-0 due to the Multiversal barriers being broken down by the Vampiric hunger of Mandrakk and the other Monitors.