Does a high "wing loading" require a high approach speed or does it cause a high approach speed?
It's the first of your options.

The effect of reduced drag with reduced wing area is dominant only at high speed, when friction drag is dominant. At low speed induced drag is the major source of drag, and with a given planform a smaller wing will create more drag at the same speed, not less.

Due to the possibility of wind shear or gusts you should keep some margin to your stall speed during approach, right down to the flare. Therefore, the safe approach speed dominates the landing distance, as Raymer writes.