The companies listed might not have attended accelerator programs, but they did everything companies on accelerators do - build an MVP, raise a small amount of finance off the back of it, iterate, iterate, iterate, get a mentor or several, iterate, network like crazy, etc, etc. Oh, and iterate. The idea, execution, timing, and luck necessary to build a company are the most critical factors regardless of where you take your first steps, but having those other things certainly helps. Accelerators put them on a plate. The founders still have to take them.

However...

<small rant>

Defining success for a business as "being a billion dollar company" is ludicrous. Those aren't the "best" companies, merely the biggest. The majority of companies aren't that size and never will be. The delusion that your new cat photo sharing app is going to propel you to startup stardom is useful at the beginning, it drives you forwards, but pragmatism is equally useful. Building a $5m company is just as much a success if it changes lives. Billionaire worship, where a company isn't a success if they don't have the potential to scale to the size of Facebook, is a dangerous thing that will, frankly, hold humanity back in the long term if accelerators take hold too much. Not every important idea is a huge world-changing event. Sometimes building a small company that makes a big difference to a small number of people is more important.

</small rant>