Seems very unlikely to me.
Both the founder (Andrew Lee) and the CEO (Ted Kim) are known in the industry, have made their views on encryption and authoritarianism pretty clear in interviews, articles, and even full-page ads in the NYT and WaPo to argue for broadband privacy[0] and encryption.
PIA also seems pretty profitable; they certainly have enough to contribute to various open source projects, join pro-net-neutrality lobbying efforts like Fight For the Future, saved the Linux Journal from death (considered an "extremist forum" by the NSA's XKeyScore), and pay to keep Freenode ticking over (they also do loads of glitzy events for the Korean-American community).
You could argue that all of this is an elaborate hoax of course, but you could do that with anything.