Well yes, Volition is totally and wholly owned by THQ. We're a true 'internal' studio (THQ has way more external studios than they do internal).
As far as what games get developed, there's a good give-and-take. They respect our abilities/opinions quite a bit, but they're also a publically traded company so they have to make decisions that aren't going to be huge disasters.
(I keep saying 'they' and 'we' because they let us operate very much as if we were independant, which is great)
If you think about it : games aren't getting any more expensive in terms of sale price. Still roughly $50. On the other hand, top end games are easily 10x as expensive as they were, say, 10 years ago. I believe the original FS budget was something in the 2-3 million range - which was a LOT for the time. These days, more and more games are having whopper budgets of $15 million+. If you do the math - that means you have to sell a ton more copies. Every project committed to is a massive gamble. Sure, the ones that strike it really big (like GTA) make unprecedented amounts of cash, but the ones that fizzle lose huge investments.