There are many ways of attempting to value a company, including looking at the discounted (and estimated) future cash flows, but they do not tell the full story.
For example, as an avid skier, I might be willing to pay $1000 for a better pair of skis as I will get more out of the ski. A beginner skier would see no increase in utility in my skis over a $200 pair. So, what's the value of the expensive pair of skis? Well, to me it's at least $1000. To the beginner, it's no more than $200.
The same holds true for companies. DCFs and multiples are useful hints at understanding the value of a company, but ultimately, they are insufficient. Companies can see strategic value in acquisitions differently, including the value of shutting it down (either because of concerns of competition or to acqui-hire the team).
On the public market, shares will more closely represent a discounted cash flow view of the future, but not always. The author's point about different share classes is also valid on public markets where control does not always go to common shareholders. That said, it's extremely hard to fool the market, as you've suggested. There's a ton of data to confirm that the market is exceptionally good at pricing the value (probability weighted against tons of factors) of future cash flows based on all current market information. There is a ton of data to support this, and very little to dispel it.