Share prices DO NOT denote actual value. Hence things like the P/E (Price to Earnings) ratio. Share prices denote estimated worth, which is often never the case (some companies trade at 30x their actual earnings, and never live up to the promise of those expected earnings). The same concept applies to public/private acquisitions.
What is actually going on with these valuations? Well, it is kind of a way of conning public markets into buying this stuff. Even in the case of "private" acquisitions, these acquisitions are largely or entirely funded with publicly-traded money used by the publicly-traded acquiring company.
This is not always devious but I suspect there are at least a few cases of corruption. Sometimes companies are innocently acquired with the true belief that they will add value. Often times, companies are acquired to simply be "flipped" - i.e. destroyed within 3 years after the shares vest. The valley floor is littered with the skeletons of acquired companies. :)
[Edit: on reading further down, the author hints at this a bit).