You are correct. Virginia, along with Georgia, Utah, Oklahoma, and Washington DC all require the taxpayer to itemize their federal deductions if they are going to itemize on their state return.
This can lead to a situation like the one you experienced where TurboTax suggests the standard deduction to maximize the federal return. However, your overall tax situation is improved if you itemize. This is most common in Virginia, Georgia, and Oklahoma where the standard deductions are much lower than the federal standard deduction.
The moral of the story is if you're from one of those three states, once everything is entered, go back and switch to itemized deductions to see if it helps.
