Harry Truman is the reason and he was merely stating the obvious.
Yes that statement has unfortunately caused much mischief in our way of thinking. The person at the top taking ultimate responsibility is the professional attitude. However, it doesn't get you any closer to determining what the real problem was, or in the alternative, why something worked well. If my assistant screws up I don't tell the judge that in court. I take responsibility for it, and I have it out with my assistant later on. I am the face of our office when in court and I am the professional, so I have to take responsibility in public. And in some sense, one could fairly accuse me of negligent supervision in a situation like that.
However, the problem of assigning blame or responsibility at the top is compounded when there are 14 layers between the person at the top and the person on the ground. There are literally millions of federal government employees. Blaming the POTUS for every error of any of those employees, or in the alternative, giving them credit for every achievement, is problematic at best. It's the same with the economy, where the POTUS isn't anywhere near wholly responsible for gas prices, unemployment, etc. It's the correlation/causation fallacy, where whoever is in office is assumed to somehow be the root cause of *everything*. We need to get a clearer sense of what POTUS's do and do NOT do, of what they can and CANNOT do. We'd make much better and more informed decisions at the ballot box if we did. Obama, for example, shouldn't be getting a 9 point bounce in approval because of OBL's death, but then again, he shouldn't be taking quite as much heat for the current economic situation as he is either.