I think you'll see the language of the EO tracks the language in the statute closely.
If the current NSA activity is clearly withing FISA, there is no reason to "keep the existence of the program secret." The existence and parameters of the program are expressed in statutory law, with a significant amount of case law now behind it.
Actually, there is. Do you remember the uproar from the intelligence community when President Carter showed satellite imagery in a press conference? As a result, certain Foreign Powers took steps to protect their assets from detection by satellite imagery...