This is an important paper. I suspect many researchers will disagree with its conclusions. But that said, its claims are profound and affect almost all PwPs, so it needs to be answered quickly.
Hinz et al. write:
"The only indication for carbidopa and benserazide is the management of ... [levodopa]-induced nausea. Both drugs irreversibly bind to and permanently deactivate pyridoxal 5′-phosphate (PLP), the active form of vitamin B6, and PLP-dependent enzymes. PLP is required for the function of over 300 enzymes and proteins. Virtually every major system in the body is impacted directly or indirectly by PLP. The administration of carbidopa and benserazide potentially induces a nutritional catastrophe. During the first 15 years of prescribing L-dopa, a decreasing Parkinson’s disease death rate was observed. Then, in 1976, 1 year after US Food and Drug Administration approved the original L-dopa/carbidopa combination drug, the Parkinson’s disease death rate started increasing. This trend has continued to the present, for 38 years and counting. The previous literature documents this increasing death rate, but no hypothesis has been offered concerning this trend. Carbidopa is postulated to contribute to the increasing Parkinson’s disease death rate and to the classification of Parkinson’s as a progressive neurodegenerative disease. It may contribute to L-dopa tachyphylaxis.
The alpha-synulcein sanity check: I don't see this as conclusive in any way, but a paper by Doppler [2] gives some support that a B6 shortage is linked to the general ill-health of PwP:
"The finding of alpha-synuclein deposits in skin nerve fibers raises the possibility of a disease-related peripheral neurodegeneration in PD. However, others found an association of the peripheral neuropathy with cumulative levodopa intake and reduced levels of vitamin B12 and B6, suggesting a pharmacotoxic cause: either due to interactions of levodopa metabolism with the methylation pathways of vitamin B12 or the interference of intestinal levodopa and vitamin uptake ".
Reference:
[1] "The Parkinson's disease death rate: carbidopa and vitamin B6"
Hinz M., Stein A., Cole T.
Clinical Parmacology: Advances and Applications, 21 October, 2014
Location from the OP reference, click on Download Article
[2] "Cutaneous neuropathy in Parkinson’s disease: a window into brain pathology"
Kathrin Doppler, Sönke Ebert, [...], and Claudia Sommer
Acta Neuropathologica, 2014,128(1)
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4059960/
John