EDIT: However...
proofer@prooferminer:~/miners/cgminer$ DISPLAY=:0 fglrxinfo
X Error of failed request: BadRequest (invalid request code or no such operation)
Major opcode of failed request: 153 (GLX)
Minor opcode of failed request: 19 (X_GLXQueryServerString)
Serial number of failed request: 12
Current serial number in output stream: 12
SOLVED

Problem summary: Upgraded Ubuntu to 12.04; found that AMD Catalyst 11.12 driver (a.k.a. fglrx 8.92) is incompatible with Xorg X server 1.13.0, which is in 12.04.2, which is the current release of 12.04 LTS (Precise Pangolin). There was also an issue of 12.04.2 having kernel 3.5, which is incompatible with Catalyst 11.12's installer; it wants kernel 3.2.
Solution: install 12.04.1, which has xserver 1.11.3 and kernel 3.2. Even after running Software Updater, which updates to 12.04.2, xserver stays at 1.11.3 and the kernel stays at 3.2. 12.04.1 is available
here.