When you go to Web Checkin after the initial time (to change seats, etc.) you'll noticed that it says "already checked in." My educated guess is that the initial check-in time remains your check-in time and that subsequent "check-ins" are just treated as changes/updates if you change seats.
Why would this be important anyway, except if the flight was oversold and you were afraid of being IDB'd? I wasn't aware that check-in time was used as a tie-breaker for upgrades as it is on CO.