Following the cash is not nearly as simple as most people make it out to be.
Fiat is a public company with an easy to purchase ADR in this country. Americans can invest in, as profit-taking owners, Fiat, Toyota, Honda, etc. Using the "where do the profits go" argument is a waste of time. You can twist the results to make any point you want to. I'd recommend basing your decision on what best supports your local economy. In Michigan that would mean the 3 "American" car companies. In Alabama it makes more sense to support Toyota.
My dilemma is this: I live and work where support for GM benefits my local economy. At the same time, I own significant stock in Toyota, the dividends and appreciation of which have allowed me to live better and spend more money here in Michigan. So what car do I buy? For me, it's just a simple decision of what car I want, which offers the best quality for the money, and which company has treated me best in the best. The rest takes care of itself.