That's the IRS answer, not necessarily the correct answer.  I think it goes back to the days when the primitive IRS computers couldn't deal with different due dates in different years.  Of course, they're probably still using the same computers.  

So they're saying if you filed on April 14, the interest starts on April 15.  If you filed on April 18, the interest starts on April 18.  But if you filed on April 19, the interest starts on April 15.  You think a judge would agree?