You also need to look at the routing rules. In this case it is a Maximum Permitted Mileage (MPM) fare.
Code:
/VIA THE ATLANTIC/ MPM 7202
MILEAGE SYSTEM APPLIES BETWEEN ORIGIN AND DESTINATION
MILEAGE SYSTEM APPLIES ORIGIN TO DESTINATION
TICKETED POINT DEDUCTION OF 2850 MILES APPLIES
WHEN TRAVEL IS VIA ATL AND/OR NYC
The trip in 5983 miles point-to-point but
north of 9,000 if routed via ATL. That's where the "Ticketed Point Deduction" comes in to play, giving you credit for the fact that Delta doesn't have other options. Putting
YVR into the mix destroys the distances (nearly 12K without accounting for real-life connections) so the fare is not valid on that itinerary. The tripled price is almost certainly BRU-YVR + YVR-SAO.