Update: I found the closest thing to a mission statement I could find buried in a wall of text on page 17 of their 2013 tax return.
Although the Phoenix Center does not meet the safe harbor test for public support (33-1/3%) in 2013, it believes that the following facts and circumstances support the organization's continuance as a public charity. The Phoenix Center has grown and developed since its inception to become a voice for consumer welfare by promoting free markets, competition, and individual freedom and liberty.
In other words, its exacta what everyone thinks. This is yet another one of those corporate mouthpiece "think tanks" that release studies to push a corporate agenda.
I think you're right about that, but that's not what the text says. Unless you think that only corporations want "free markets, competition, and individual freedom and liberty". Corporations typically want none of those things. They like markets that benefit them at the expense of their competitors, not free markets, and they'd love to have no competition. They tend not to care much about individual freedom and liberty, except to the degree that their directors feel personally strong about such issues.