Even though the sun is not illuminating the shadowed area, you can still see plenty of detail in it so something must be illuminating it. That something is light being reflected from the blue sky above it. Therefore, light in the shade is composed of a large percentage of blue light because it is being illuminated by a blue light source- the blue sky. For many subjects, you definitely do want to take out or at least eliminate some of the excess blue light. But, you can use this natural blue light to advantage as well for certain subjects.
Blue flowers are often tough to record properly on film.
Many blue flowers tend to record on film with a strong magenta cast. Perhaps you have noticed this before. I have photographed bright blue hepatica and violet flowers that recorded bright pink on slide film. My solution for keeping blue flowers blue on film is to avoid photographing them in sunlight or on overcast days. I always photograph blue flowers in open shade situations such as on the shaded side of that maple.