I think going the entertainment/easy-going angle is best. It's supposed to be a fun Netrunner side tournament, so a relaxed atmosphere is best. It would feel very odd to see a very entertaining and fun match shortly followed up on the ramifications of Edward Snowden's actions - or nations' policies regarding killing people in other parts of the world. I would certainly do a double take.
It would be like sitting down to watch a football game, and then during halftime, Fox shows a pre-recorded session of Joe Buck and Troy Aikman talking with Aaron Rodgers about US foreign policy. It's like..."What the hell? I came here to watch football. And hear people talk about football."
If you feel the need to discuss something serious, it should either be absolutely huge news that transcends card games (IE Columbine, Sandy Hook, 9/11 type news), or probably at least be related to Netrunner in some way (the big movement we had with a code of conduct, or possible cheating, or even money prizes, since that's been approached before). This is how professional sporting events handle their broadcasts; I think it's probably correct, and we should follow their example. We take ourselves seriously, and others will take us seriously too (probably preaching to the choir).
Other topics could totally be covered, but I wouldn't do it during the Netrunner stream, maybe either after or before the games themselves start up. It could be like another segment "Perspectives from the Community" or something, where we can discuss the serious issues together.