"The gene for vitamin C" is rather woefully misleading. There are several different enzymes
involved in vitamin C synthesis
and the majority of them function just fine in humans.
There are two steps in the pathway to produce Vitamin C that are damaged in humans. The first is universally prevalent. The second error is known to be totally eliminated in some populations.
The error is in the gene for L-gulono-gamma-lactone oxidase. This is the last enzyme in the ascorbic acid synthesis pathway. The reaction L-GLO catalyzes (production of 2-keto-gulono-gamma-lactone) will also occur spontaneously on its own, so humans do in fact produce small amounts (15-20mg per day) of vitamin C. L-GLO is pseudogenetic in humans- no alternative product occurs.
The second error deals with lactonase. Lactonase is the enzyme preceding L-GLO in the chain. If functional it would dehydrate and cyclise L-glulonic acid to produce L-gulono-gamma-lactone. Mutants of this second type produce no ascorbic acid and must get it from external sources lest they develop a health threatening deficiency.
Quite predictably, the prevalence of lactonase dysfunction can be highly correlated with the availability of vitamin C. In certain tribes of desert nomads the dysfunction is totally absent. It has been predicted that historical seafaring communities would have also had a higher percentage of functional lactonase enzymes due to the disproportionate loss of sailors with the malfunctioning allele because of scurvy.