Is investing in foreign companies in US markets the same as investing in those companies in other markets?

I just switched my portfolio from an S&P 500 fund through Fidelity to a Fidelity fund that invests in international stocks. But that still invests in those stocks in the Dow Jones or Nasdaq right? Which means that if people sell out of the Dow Jones or Nasdaq, my portfolio still goes down right because the stock price on the Dow isn't linked to the stock price on day the Nikkei?

I guess what I'm trying to ask is moving my money out of a US dominated fund like the S&P into a bunch of international stocks worth it when it's still through an American exchange?