Conditioner doesn't have to be applied to wet leather. The advice was only in the context of washing (and rinsing) shoes.
The conditioner will slow the evaporation rate and allow the water to spread out through the fibers of the leather more evenly. It helps to prevent water stains.
Water stains are the result of salts and other chemicals dissolving in the water and being transported to the interface between wet and dry. One such interface is the grain surface of the leather. Another is the edge of the wet area. If water evaporates too quickly, the stain occurs just at that interface. Such stains can be difficult, sometimes impossible, to remove.
Casual washing and rinsing may not create water stains but it is always better to be safe rather than sorry. Hence the conditioner.
In any case, applying the conditioner while the leather is wet won't hurt anything. In fact, when the pores are open and cleansed of residual oils and waxes the conditioner will enter the leather more easily.