IRS Letter 4870 question, part 2

To add to previous message (IRS Letter 4870):  

The IRS letter was dated April 11, but of course, I received it on April 16 (the day after the deadline).  I wrote a paper check and mailed it immediately via certified mail, but by then my payment was late and a penalty was assessed.  

My question:  Could this have been a Turbo Tax problem?