Would you turn down a "name your price or we'll run your business into the ground wink wink" (by disabling app store, never getting on the first page to results, etc). Not saying that is what is going on or anything...

In most cases the underdog is running on investment funds, and has handed over a significant amount of the company control to investors. When a buy is proposed, those investors have to weigh the really quick (probably really large) profit of selling versus playing the long game fighting an uphill battle against the giant.

This is how promising companies are swallowed by the market leaders.