The only advertising that is obvious, is the advertising that is obvious. There is an enormous amount of money spent by advertisers that is far more subtle, from product placement, to "viral" marketing. In this age where people commonly walk around with their faces buried in their cell phones, advertising is more, and more disguised as something else.
I wonder what part of the military's budget these events came out of? I would assume it was part of their recruitment budget. But, regardless, I would also assume that the military felt like they were getting something out of this.
Time is money, as they say. If an NFL team is using up time to promote the military, be it a recruitment commercial, or an "honoring our troops" event, they are still providing a service. Why shouldn't they be compensated?