Yes, you're right, I was not precise. That's what they used to say about themselves:
“The Vanguard Group is truly a mutual mutual fund company. It is owned jointly by the funds it oversees and thus indirectly by the shareholders in those funds. Most other mutual funds are operated by management companies that may be owned by one person, by a private group of individuals, or by public investors. ... The management fees charged by these companies include a profit component over and above the companies’ cost of providing services. By contrast, Vanguard provides services to its member funds on an at-cost basis, with no profit component, which helps to keep the funds’ expenses low.”