It would be cool if Media coverage can be used to turn a military defeat into a cultural victory or a Military victory into an even bigger victory. For example:
If you have enough points in "Media Spin" you can chose to make the loss of a planet look like the Alamo, and your people will be whipped into a patriotic frenzy increasing allegiance (and thus income) for a while, and making more people in nearby planets volunteer for the planets militia, making it harder to invade, and making tactical structer cheaper around nearby planets since the people would want to make it easier for you to defend them. To balance this you could make it so that you could only glorify a defeat every so often, or make it so that if you don't go back on the offensive, and take back that planet (and maybe another one) soon, your people will see you as a weak, incompetent leader (turning their sensationalism against you) This would lower their allegiance to lower than it was before the loss of the planet.
Then you could have "Offensive Media" which would affect how other empires view yours and vice versa (putting it higher on the tech tree). So if we take the same situation where you've lost a planet; the enemy, if they have enough points in offensive media, could start a propaganda campaign, where they constantly tell the people that you suck as a leader and that you can't defend them so they should rebel. Of course (read: for balancing purposes) your people wouldn't really listen at first since there are setbacks and defeats in war, but if the enemy captures say three contiguous planets in a row you suffer an allegiance penalty. This can be turned against the enemy by breaking their (military) offensive. This would prove to your people that you are there to protect them, giving you a permanent allegiance bonus and making it harder for another propaganda campaign to be successful.
Of course this whole media system could be completely circumvented by having a military so strong that the bonuses and penalties wouldn't make a difference. This system is essentially like taking out a loan. If you think that you can break an offensive, than the media spin power could give you that extra boost to make that happen, as well as give you some extra cash, but if your fleet is on the other side of the galaxy, and you left a weak spot open. Then the power can only hurt you. Same with the propaganda campaign, if you take a planet, but know that the enemy's fleet is just a jump away, using the propganda campaign power would not be a good idea.
Man, that was a lot longer than I thought it would be