The problem with making the access of public, unclassified systems punishable by UCMJ seems obvious to me. I do not think you agree with this being a problem. I'm open to your exposition and I hope you are to mine.
If tomorrow is the day that Greenwald will publish Snowden's leaked information then today the Guardian is a website that a solider can access without UCMJ consequence. The common soldier does not possess a security clearance. Among those who do, they do not have access to the material Snowden leaked. That is highly compartmentalized. Therefore, even soldiers with a Top Secret (TS) clearance would not recognize classified information leaked by Snowden as being authentic. The information is on an unclassified system on non-mil, non-gov domain. Greenwald and Snowden claiming it is leaked classified material isn't sufficient for a common soldier to regard the data as such. This requires verification by senior commissioned personnel. Command must inform unwitting soldiers that the information they are reading is classified. Until they do, the soldier cannot be certain. This is effectively classifying any information published by the Guardian as TS. It is unlawful, then, for the soldier to use an unclassified system to access a classified system. If this was only about justifying a block or filter then there'd be little to discuss. But this is about making the soldier's exposure to classified information unlawful, witting or otherwise. Most problematic to me is the fact that command issued this statement to formally classify the information as the soldier is concerned. That is one shade of grey apart from command divulging classified information to personnel that do not possess the clearance.
Command recognizes that they are partly corroborating Snowden's leak if they specifically refer to the content of the documents. They've been careful to cover their ass, though. Instead of explicitly citing the classified information, they classified the source- the entire system. This is the precedent that concerns me. This is command classifying information to empower them to leverage the maximum authorized penalty under UCMJ. This is worse than censorship. This makes reading certain public domain a criminal act.
To your final point I cannot understand your reasoning. Yes, it is a voluntary act. It is a service that people volunteer for that benefits the entire nation. It benefits many other nations. And for this you want to strip them of something? These individuals volunteered to be engaged in the needs of the military. That's to say they aren't guaranteed they will be or do any particular thing. They will be and do what they are told. In some situations that's compromised the individual in ways that would be criminal outside of service. And to that we say, "you volunteered and signed your life away"?
The soldier volunteered to do a job others wouldn't. In cases like these, the soldier hopes civilians will volunteer to do what they cannot. I elect to speak out against this and demand clarification. I charge this is unlawful and dangerous beyond any soldier reading a website might be because the soldier cannot.
What course of action do you propose to a soldier that might be reading this? If what was happening was unlawful in your eyes, what would you suggest is done by the soldier?