However, exercise has been shown to significantly improve bone density.

Specifically, exercise has several very concrete physiological benefits including improving mitochondrial density (which improves energy production at the cellular level). With regard to bones, even mild exercise has been shown to have a significant positive impact on bone density and a reduction in the likelihood of injury.

My understanding is that calcium intake is only one part of the equation. The other is calcium up-take. It would seem exercise works on the uptake side.

Possibly these studies are flawed if they are looking at intake without looking at uptake (corrleated with exercise) side of calcium.