I don't follow your logic at all. If the 87% is achieved by control of the media and propaganda, it is not a representation of inherent support but only a measure of the level of dominance of your message control, and likely, the ability to create a strong fear of not answering with a thumbs up and a smile. In other words, it ceases to matter if it's measured accurately or not, because no one should care about what it measures.

It's like doing a survey on how much people like a restaurant where if someone gives a five star review they get to enter a sweepstakes to win money, but they get no entry if they answer four and a half or lower. Wow, we got 4.8 stars, we're awesome! Pat on the back to us!