UPDATE: It seems the issue has something to do with a hardware date reset to 12/31/99 (per my own "fat" retail and debug units) that occurred with the February 28 to March 1 turnover, even though this wasn't a leap year. I say 'hardware', because it reportedly occurs whether you've gone online with your PS3 or not.
It's not the first time the error's occurred. Run a date-filtered Google search on error code '8001050F' and you'll see it popping up time and again. Sounds like we'll either need a 24 hour cycle or a firmware update to see this fixed (and no, manually setting the correct time and date doesn't fix the issue).
UPDATE 2: Wondering whether Sony could remotely patch an issue that prevents connecting to the PlayStation Network? I assume the firmware update process works discretely, since clicking 'System Update' generates a standard "There is no need to update" message and not an error.
UPDATE 3: According to The Examiner, Sony tech support says both trophy and savegame data should be fine, and that a fix should be up 'by morning' (US time zones).