Incidentally Vanguard et al have no managers in that sense either - they just track the indices.
I don't think that's right. Only the specific funds (e.g. the Vanguard 500 Index Fund (VFINX)) that say they track the indices do that (and generally charge a lower 'management' fee). Most funds (e.g. the Vanguard Capital Value Fund (VCVLX)) try to beat the indices, charge higher fees and have a range of things they are allowed to buy. There's the control.
From the wikipedia page (which lines up with my knowledge): Since its founding in 1975, Vanguard has grown to become the world’s largest pure no-load mutual fund company. While mostly known for its low-cost index funds, Vanguard also offers a variety of low-cost, actively managed mutual funds and a line of exchange-traded funds (originally branded as VIPERs.) Vanguard also provides brokerage services, variable and fixed annuities, educational account services, financial planning, asset management, and trust services.
I believe you mean that their managed funds use an index as a benchmark.