The key to the Toyota method is that over time, it results in fewer line stoppages overall, because real or potential problems are identified quickly.

If a bolt is hard to thread, but you never stop the line, you're going to get a lot of crossthreaded bolts. But if you stop the line for every crossthreaded bolt, the company will very quickly realize they need to spec or design a better bolt.

So, the "anyone can stop the line" mindset only works in the context of a management philosophy that values continuous improvement.