Honestly, if the highly regulated Chimp SSP say she is 71 I would tend to believe them.
I would say that if this chimp isn't 71 then its because of innaccurate records of her earlier life, rather than a deliberate effort to mislead. I think even a commercially driven Safari park(as they all are) is unlikely to give such a precise age for one of its animals unless it at least believes it is true. Whether she is really such a great age is debatable perhaps.