Only mentioned in the first book, "Created, The Destroyer", the Folcroft Foundation is a secret group that funds Folcroft.  The idea of CURE and Folcroft transformed after the first book. In #1 Folcroft was a military like, high security training ground for special operatives.  Remo was just another trainee from a "special branch" of the compound.  Technically CURE was not only known to just The President, Smith, and Conn - the entire foundation knew of it as well.

We can only assume that the many agents CURE had (active agents, not information gathering) also knew about CURE.