Why is it difficult to bend the waist while keeping the knees straight?
First off, I would be careful generalizing people's experiences with this exercise (..."Try it...You'll have trouble long before you reach 90 degrees"...):


Source: Yoga Tune Up

The muscles you are feeling at 90o, and the lady pictured above perhaps not even at 180o are the hamstrings. They run along the back of your thigh, attaching at both the hip and the knee. They flex the knee and extend (straighten) the hips. 


Source: Precision Nutrition

When you do the exercise you are describing, the pelvis starts pulling on the hamstrings from the top because your knees are staying in place. Bending the knees releases the stretch.