"I think that the fact that there is so little documentation such as who, what unit, and so forth fired that deadly shot.

It is documented fact that the 18th North Carolina was the unit that fired on Jackson and his escort.

Jackson died as a result of "friendly fire." He was shot at Chancellorsville on May 2, 1863, by an unknown member or members of the 18th North Carolina Infantry Regiment... See Source Below

"Think of the remorse and demoralization that would have came about if it had been narrowed down, as I'm sure any investagation would show."

"The order to fire was given by Maj. John D. Barry, and many of his men fired at the same time. Jackson was struck by three smoothbore musket balls. Barry died two years after the war at the age of 27; his family believed his death was a result of the depression and guilt he suffered as a consequence of having given the order to fire."... See Source Below

"Actually I beleive there was an investigation and it concluded he was shot by his own pickets."

Since it was Jackson's corp that had made the famous flanking move that resulted in their being there it is only logical to say it was his own men who fired the shots. Longstreet and his corps weren't even at this battle and the other troops in the battle were under Lee's direct command. In fact after Jackson was wounded Lee put his cavalry commander, J.E.B. Stuart in command of Jackson's Corps.

Still going to borrow this for one of my front porch yarns..."

My opinion, that is all this is... a yarn.

Source: Virginia Military Institute...
http://www.vmi.edu/archives/Jackson/tjjfaq.html