The paint damage points to a leaking rudder PCU in the past (though I can´t make out any currnt leakage on the picture), Skydrol hydraulic fluid has the properties of a good paint stripper, and the damage is right beneath the access panels for the rudder mechanism.
Concerning the idea about paint damage through heat from the APU exhaust, this is utter BS
First, the APU is sited aft of the damage, secondly, it is encased in a stainless steel APU compartement (to contain a possible APU fire). During APU operation a fan blows continously cooling air through this compartment and overboard through a hole on the left side (just aft and below the elevator). The APU exhaust pipe is even further aft and is insulated.
If the heat in this compartment would be high enough to cause damage, the APU fire warning would go off.