What does it mean when a track "straddles north"? Have heard a couple controllers taking note of a track that "straddles north".  What do they mean?

According to Google, the definition of the verb straddle is to extend across or be situated on both sides of.  Cannot see how this would relate to a track.
So the problem is that cruising altitudes are assigned based on heading E or W. If the desired track is within a few degrees of north or south, the heading needed to maintain the track could 'straddle' north or south. With some tracks/wind combinations two aircraft flying the identical route at different airspeeds could fall into opposite hemispheres. Traffic in the reverse direction has the same issue, possibly resulting in opposing traffic at the same altitude. So which altitude do you assign/use?