The question is can the White House order Petraeus not to testify on the grounds of national security? If yes, could he still be forced to testify in a closed session of the House Intelligence Committee? And if he does testify in this manner, will the true story just be buried by cowardly House Republicans?
The answer is no to that. If it is deemed a security risk they can do it behind closed doors, although I doubt the GOP led house would allow that.