So, the State is not using the federal money its entitled too? That's not cool. Its bad adminstration by the states. The states adminster the federal program.
However, the point is that you asked why they would have ads on TV promoting food stamps. You gave us very little information, other than your personal recollection of the ad. So, I had little to work with.
To answer your question, I provided a serious of credible, and linked reasons from officials: stigma, beaurcracy, etc.
Given the minimal information you provided, I think those are valid reasons they might be doing outreach. It certainly doesn't sound as far-fetched as the reasons you guessed at.