Although the OD Cost Matrix tool shows straight lines connecting origins and destinations, the it calculates the network distance or travel time and reports those values in the output table. The straight lines are intended only for visualization, like a spider diagram.
If you need to use the output of a network analysis to determine which countries the route goes through, you cannot use the OD Cost Matrix tool. OD Cost Matrix only reports the travel time or distance and not the actual route.
You should instead use either the Route solver or the Closest Facility solver, depending on the way your problem is set up.
