I think that it probably is a coincidence.

Asparagine is an amino acid which is found in almost all proteins. What the recent papers show is that AEP can cleave two proteins (Amyloid Precursor Protein and Tau) at specific asparagine residues, which promotes formation of neurotoxic species in AD and the same applies to cleavage of α-synuclein by AEP in PD.

Although fructose-asparagine is inflammatory I don't know if it can enter the brain. If it can I would expect it to have systemic effects rather than specific effects as in PD and AD though I could be wrong about this.