Again, I'm pretty sure that the military will not hold you responsible for something you were shown. That is, I don't see how they would hold someone responsible for being accidentally exposed to something on the morning news. That said, there are many articles from around the Snowden times that talk about the Navy and Air Force blocking wikileaks so that people won't expose themselves to things outside their sec level. Here's one I was able to find from around that time:
http://www.nytimes.com/2010/12/15/us/15wiki.html .
It might seem backwards, but members of the military are subject to trial by military tribunal. They agree to this when they sign up, and you agree to more restrictions on your actions when you apply for security clearances. I don't know specifically what they are and I am not a military lawyer, but I have five or six friends who have at one point or another had S or TS clearance in the army, navy, and two other three-letter agencies and have had casual discussions with them about it.
tl;dr: You agree not to read things outside your security clearance when you get one. If you do so, you're subject to legal repercussions. It's my understanding that going to a website and knowingly downloading these things would be treated similarly to reading something using a coworkers network account that has access to a higher security level than your own.