TurboTax determined that I did not owe a penalty, yet the IRS just sent me a bill for one anyway. Who is wrong here?

[Critter]

Neither are wrong ...

The TT program calculates an estimated underpayment penalty based on the entries you made in the program however the feds & state reserve the right to bill you for underpayment penalties based on the info they have (which may be different from what you entered) and when the taxes where actually paid.  Also they will calculate late filing & late payment penalties and add interest as needed.