I've never heard of the 13 parr marks theory!
Here's what Dr Peter Moyle has to say: "about 10 parr marks are usually present, even in adults, centered on the lateral line". The Golden's I submitted for my HTC had 12 parr marks (and I got the HTC)!!!!!
AFAIK, per previous discussion with Roger Bloom DFG, the only HTC species they apply a "purity test" for qualifying for the HTC is Paiute Cutt's. They must have under five spots total per side or are considered Lahontan hybrids. Otherwise, location where the fish is caught is the only criteria looked at. Must be true, because my KRR looked nothing like they were supposed to, but did come from a historical drainage!!!