Take a simple ecommerce AB test as a starting point. Should our shopping cart look like A or B? Apply Bayes theorem and it doesn't take that long to gather evidence that A increases conversions by 1%.
Now replace the simple AB test with a multi armed bandit.
Now run the multi armed bandit continuously across all social media platforms and keep tweaking to maximize sentiment in your favor.
That's even without applying data science to the social network graph.
The "fundamental problem" that you lay out is definitely related. The "fundamental problem" is that we are so susceptible to such algorithmic manipulation.
Anyway algorithmic manipulation isn't limited to just facebook, the data that enables it is generated on many other platforms.