And in the case of Russia shutting off the external connections, thus preventing any external news agencies from reporting, the Russian stock market would happily continue on?
Unlike the US and Europe, capital in Russia is largely stashed abroad, and the economy not especially dependent on the small amount of trade and information mediated by the domestic stock market.
A stock market is kind of an institutional miracle -- people who don't know each other come together in the form of corporations, and then borrow from other people that don't know them. In a place with less trust, such cooperation is less feasible.