When I look up the income from 1040 line 15, calculated by turbo tax, with 2020 Tax Table line 16 don't agree. Turbo Tax, line 15 shows $11,156 and the table lookup would be $11,562 for a difference of $406 in my favor. For my mother in-law Turbo tax, line 16 shows $0, the table lookup based off Turbo Tax line 15 the table look up would be $533. Why are they different?
Some of what you posted doesn't make a lot of sense.. ( "Turbo Tax, line 15 shows $11,156 and the table lookup would be $11,562 for a difference of $406 in my favor."................ line 15 or line 16 ?? )
BUT...you may be making a mistake of thinking that the line 16 $$ value uses only the tax tables for line 15.
what many people don't realize is that $ on line 3a, and any long term capital gains as a part of line 7, are included in taxable income, BUT, they are taxed at a lower rate...so the tax tables aren't used on the entire amount of line 15.
Certainly there may be other mistakes from data entry, or bugs that can affect the tax calculated on line 16, but so far, no one has found an issue with the actual tax that TTX calculates.
IF you print out copies of your files with all forms and worksheet, there should be a tax calculation sheet that shows that the tax tables were not directly used....unusually it's a "Qualified Dividends and Capital Gain tax Worksheet"