I profess ignorance of the May 13/14, 1863 events. However, your comments I quote below, do not seem to fit the question?
Bearss is still active, I suggest you question him. Or Terry Winchel, Historian at the Vicksburg National Military Park.
"I have pretty good evidence that McPherson captured Colonel J.B. Robertson posing as a civilian during McPherson's feint on Canton in October 1863. Shortly after McPherson captured Robertson, the expedition came to a sudden end, and McPherson returned to Vicksburg.
"McPherson never reports why he decided to withdraw back to Vicksburg; his list of Confederates captured does not include anyone with a rank above lieutenant. J.B. Robertson would survive the war, so obviously McPherson did not have him killed. One can only assume that Robertson reported that Loring was on the way with all his available force. McPherson's objective accomplished, the federals returned to Vicksburg and Robertson was released."
These quotes do not seem to relate to the May event in question.