After further investigation, it appears that TurboTax calculates the effective tax rate using the total tax on Form 1040 line 24, not the tax on line 16. Divide the total tax on Form 1040 line 24 by the Adjusted Gross Income (AGI) on Form 1040 line 11 and see if you get 6.15%.
I have added an update to my earlier answer above to make this change.
