No, you aren't crazy. However, even if Vanguard went belly up it shouldn't affect your investments. Vanguard's assets and their customer's assets should always be kept separate. They can't use cash from your account to pay staff salaries, utilities, or anything else. Barring fraud, a bankruptcy of Vanguard should not affect your assets.
That said, I have accounts with both Vanguard and Fidelity for a couple reasons. First, the aforementioned though extremely unlikely fraud scenario. Second, and more concerning to me, is outside criminals hacking into an institution and wreaking havoc.