Sounds like the old concrete walls were covered up possibly with foam sheets then a finish stucco applied.
Guaranteed those woodpeckers wouldn't be beating any holes in concrete, or concrete block either.
Tap on the wall, does it sound solid, or sort of a hollow sound. You could even drill a small test hole to check whats under the stucco finish. Original wall might have also been stripped with wood furring, then sheathed with something and that covered with wire lath, then coated with stucco. Normally that type system wouldn't extend all the way to the ground causing a step in the wall just above ground level.