I don't think you have to be invited. Though it's probably hard to get a meeting, just like it is with any VC.

Google Ventures is fairly similar to traditional venture capital, but with more support provided to portfolio companies. Andreessen-Horowitz is another VC that follows this model. Besides providing traditional VC help (money, intros, executive recruiting, advice), GV and A16Z have operating folks on staff that can help portfolio companies with things like HR, Bizdev, engineering recruiting, UX, etc.

Aren't all funds, in a sense, like that?

You typically get much further from an invitation or an introduction than anything else.