A base neck level for a '63 would be considered on the low side of normal, but not necessarily indicative of poor storage, moreso 42 years of bottle age. Anything younger should obviously be higher up the neck. I have had VPs from the '20s and '30s that were also base neck, so it stands to reason that Port is a hardy lot and the corks used for VP are normally as good as any produced. Having had my share of 19th century VPs, I will say that very few were recorked. High quality storage conditions remain the integral component to fine old VP, not corks, although they do count.
Outside of Madeira, I can't think of any other wine except possibly Sauternes and Tokaji (maybe Riesling) that can possibly hold together as well as VP. Even these others are less likely to show as well with 100+ years of bottle age.
Of the bottles of VP that I have either opened from my cellar, or been a part of from others, I have had only about a dozen corked bottles out of somewhere around 1300 bottles. That includes 3 corked bottles (in a string of bad luck) of 1983 Cockburn's ... all from my cellar.