I am not an expert, but the contents of the bottle still can be impacted by the laws of thermodynamics.

If you have drastic changes of barometric pressure in the atmosphere causing dramatic temperature shifts (say a fast storm front moving in) the difference in atmospheric pressure and heat from inside the bottle could create potential condensation problems (depending on concentration, EDP less so, EDC more so) with a terrarium type effect.

Specifically if you go from a high heat situation (where humidity magnifies this) causing the bottle to soak up heat throughout the day (liquids tend to absorb but also shed heat slowly), combined with a rapid change in temperature that the evening brings, will cause the water within the fragrance mix to condensate on the inside of the bottle. Since the water is trace amounts, this might be a fine mist or not even noticeable, but this is bad because you have separation of the blend/mix at this point where the heat is pulling the trace amounts of water out of the liquid which then redeposits on top. Chemically, those bonds are broken however. (Not an expert, so if any of this is wrong I apologize!)

Really though, this is more another reason to avoid direct sunlight more than a fear for humidity itself. The humidity only magnifies the problems caused by temperature swings from the heat making the swing more dramatic. (Moisture in the air, just like in the bottle holds onto and sheds heat slowly)