Vanguard isn't lending you money when you open an account, so I don't follow why they'd investigate your credit. Most often, your money flows into Vanguard funds, and waits for you to sell it at a future date.
Vanguard does have an option to open a checking account, and do offer "margin loans" if you sign an agreement and have assets to loan against. But they aren't relying on your creditworthiness. Even for margin loans, they are loaning you based on assets you hold at Vanguard. If you don't pay the margin loan, they sell your assets to pay it back.