I also found LanChile's routemap to be a work of fiction (oops, that should probably read 'slightly free with the exact truth').
I asked them about the CUN-HAV route which they show, and they don't fly that either

Basically, they said that the timetable shows where they fly, the route map is just a 'guide'.
hth
Stewie
PS I agree with christep - you've only got 4 segs in SA.