I think Charles is playing 'em. A few years ago, there was a question of whether he should be "Defender of the Faith," the nominal head of the CoE, with his divorce and his documented adultery -- now he's got 'em down to arguing over a definite article.
The title of "Defender of the Faith" was first bestowed on Henry VIII by the pope, because of his defense of the Catholic view of the Eucharist against Martin Luther. Henry VIII later had Sir Thomas More and Bishop John Fisher executed because of their loyalty to the Catholic Church. It seems ironic that the non-Catholic monarchs of England have continued to use a title which came from the pope.
Since Latin doesn't have either a definite or an indefinite article, Defensor fidei could mean "defender of a faith"--so whatever faith the heir apparent has, he can be the defender of that.
It was most certainly not an hereditary title but Elizabeth I acted as though it were while maintaining her major hobby of causing Roman Catholics to be hanged, drawn and quartered before being disemboweled for saying Mass in Great Britain. Just another case of grand theft ecclesiastical.