One major reason for the classic FBI tilt was that the FBI taught using the crouch stance in which the shooter goes into a crouch position.
That was covered by Cuningham in his book. He stated that everyone goes into a crouch when startled and it is as you said, tilt is better than strait when crouched. However, in some scenarios, I know that I would not crouch. If someone shot at me, I would most certainly crouch instinctively as he asserted. However, if I was in a parking lot at night and someone came close with a knife, club, etc. and demanded my money, I do not think I would be in a crouch. Again, there is the difference between his and my frame of reference.