It isn't false at all -- it depends entirely upon the geometric relationship between the center of mass, and center of lift. If the center of mass & center of lift lie on the same horizontal plane in an aircraft with zero dihedral, pitch-up results in virtually no longitudinal change in that relation ship. In cases where the center of mass is vertically displaced from the center of lift & either dihedral, or anhedral are present, pitch-up will shift the center of lift axially relative to the center of mass. The longer the wingspan & the greater the dihedral, or anhedral angle, the greater the longitudinal displacement. Anhedral shifts the center of lift forward & dihedral shifts it aft.

Anhedral destabilizes aircraft in both roll & pitch.