The answer to this can be VERY complicated, but you can start by comparing what you find in desc=74 of the MD file with the fastest lap time you are seeing on the track in qualifying.
Desc=74 is on line 76 of the magic data file and it defines the fastest qualifying lap time in seconds, so 69560 means 1m 9.560s.
(The value in desc=74 actually adjusts the game clock, but we don't need to go into that now. The point is, the game uses the value in desc=74 to determine what constitutes ONE LAP for the purposes of multiplayer mode, NOT the actual lap time on the track).
Therefore, the time you see on the track should match the value in desc=74 (roughly) - and if it doesn't, it explains the problem you are having. So in your case I'd expect to see a big difference.
If your track doesn't have a magic data file you can make one using
cmagic