I don't think that this shift has anything to do with cross-link density. This rather seems to be a measurement of the nanoparticles' diffraction pattern. You can determine the degreee of crystallinity with SAXS, but not the cross-linking density and not with XRD. I wouldn't necessarily believe the interpretation of the authors.
I think the difference in XRD shift is because of a change in crystallinity. Then, they hypothesized that this change is because of crosslinking between nanoparticles and hydrogel chains. Am I right?