Well, two reasons for the validity of the answer, it is true indeed.

Wing bending moment. In the image above (earlier used in this answer) it shows the bending loads from lift, distributed over the wing. So the wing is loaded in bending, the bending moment is countered by the wing skin panels. Causing tension in the lower wing area, compression loads in the upper wing area, which has to be dimensioned for buckling under 2.5g loads.
So one could still maintain that the wing skin panels are under compressive loads, not the case for…..
Shear. Wings not only bend upwards, but twist as well. Due to the constant $C_M$ of asymmetrical profile wings, the wing tip wants to twist to a higher AoA, causing shear in all the wing panels. If the shear stresses exceed the dimensional/elastic buckling dimensions of the wing plate, it will deform in a wavy pattern, which is also a form of buckling.
So yes, wing plates can buckle without compressive loads, from shear stress. The good thing is that plates that are supported on all sides can still carry stress when buckled, unlike a long beam supporting a vertical load.