Technically speaking, any information might aid terrorism...
That seems to be a fairly vague claim. The issue should not be whether or not such information motivates terrorism but whether the individuals who divulged such information were actively seeking to aid and abet terrorists. This is suppose to be how the criminal justice system works (yes, I understand we are entering the realm of international politics and law). A crime generally speaking exists because of intent.
How likely is is that people like Miranda were actively attempting to divulge classified information to terrorists? Exceptionally low. So low as to be no different from zero.
These anti-terrorist laws thus become nothing more than a trapdoor to gather information that would otherwise be unattainable. That simply cannot be allowed to exist in a just society. If the state wants to confiscate a private citizen's property, they should be required to put forth some sort of meaningful justification. Without that, we are all targets because any dissent could be construed as anti-state and pro-terrorist.
We are walking on very unsure earth at this point.