There's also the part 2. Check it out.
The whole idea of this loose structure is based off trust. Without trust, this won't work. So obviously, if you have an enormous company with poor management teams and where 50% of employees aren't happy, you can't just switch to this structure and expect everybody to get happy and get along. This is something that has to be built from the ground up, starting from the core original employees, and the support from the management.
Managers of a Big Co sometimes want to keep that power. Why? They don't trust their employees will do the right thing. They treat them like some kind of farm animals, resources that needs to be caged and directed to maintain order. This is fine and well, but domesticated employees will do nothing but being told. Without direction, they will refuse to work. When there is no project to work on, nobody will come up with a new exciting project, people will simply sit and idle. Not because they can't start one, because they don't want to. Why should they? They don't get paid extra for it, and perhaps if the project did end up successful, the managers or other people will try to steal the credit -- because there's no trust among the employees.
While a structure that's as loose as Valve's encourages employees to be independent, so they can have some 'ownership' or 'investment' to their projects, which ultimately benefit the company as a whole. The idea is for employees to understand that the company trusts them to do the right thing, and that they should be the one turning the gears, not being the cog in the wheel.