Sorry, but no one controls the internet. "They" may have some power over DNS (the name to number translation network), various TLDs (.com;.mil;.edu;.net...), many back bones and even some power over various large scale ISPs... but that's not the entirety of the internet.
Just like they can flip a switch and kill all .com or .mil traffic on a certain leg, we can flip a switch and avoid using it. People have just become so enamored by its utility that they forget it's really nothing more than you connecting your computer to mine. Extend this to cell phones and you find that with one simple mesh app, entire cities could connect their cells and WiFi networks into their own internet, all for no cost. Add in a few hardware additions and you've got satellites, radio, laser, light and other city-to-city connections. This is the exact method that Africa will use when they take over internet dominance (adoption rate) almost overnight.
However, your position is that we don't want our money dependent on the internet? Sorry to disappoint you but it's been so for years. Most large companies do payroll via files transferred online. All companies that I know of manage their multiple bank account actions via the net. If anyone took down the whole internet, the entire modern world, including governments, would screech to a halt.