There is so much to take in, review, and respond.
The whole cavalry episode is contradictory. Rawlins, in his attempt to scapegoat Wallace, wrote about the cavalry officer: "This officer returned between 12 o'clock m. and 1 o'clock p. m., and reported that when he delivered your message to Major-General Wallace he inquired if he had not written orders. He replied in the negative, and General Wallace said he would only obey written orders." There seems to be no corroboration for this version, besides Rowley's similar attack on Wallace, which included: ""Shortly after the hour of 12 o'clock m., as we were riding towards the right of the line, a cavalry officer rode up and reported to General Grant, stating that General Wallace had positively refused to come up unless he should receive written orders."
And this severely conflicts with the account by Bennett: "Lieutenant Bennett delivered his message and the order was at once given to fall in line. Wallace's command started out ahead ...." And Bennett's account in Fletcher has problems of its own. He makes it seem as if they road to Crump's and met Wallace, who was already at Stoney Lonesome by this time. He states: "We retraced our steps therefore, to the junction with the River Road ...." but Wallace's counter-march turned right before reaching Stoney Lonesome. Bennett also wonders why he was not allowed to lead Wallace back on the River Road and said Wallace took the wrong road. This indicates that he had no knowledge of the Shunpike vs. River Road issue, which is strange and also makes his opinion suspect.
There could be a discussion of why Grant, who with all of his staff appeared to forget to carry writing materials with them, gave such a threadbare order to Bennett. "Present my compliments to General Lew Wallace and tell him to come immediately, you being the escort," doesn't indicate the route, the urgency of the movement, who and what to bring, the destination, or what should be done upon arriving.
The edited portions of Hurlbut's post-war account of Shiloh indicate that Wallace was expected to arrive via the Shunpike:
"Within half an hour, about 10:30 am, the enemy captured Behr’s Battery under circumstances not creditable to the artillerists, and forced Sherman to take up another line of defence. Up to this time General Sherman had been able to hold the bridge and road by which Lewis Wallace was momentarily expected, and it was with the greatest reluctance, he was compelled to abandon this means of communication and possible relief."
"About 10:00 am, General Grant rode up and inquired into the situation. In reply to his question: “How long he could hold out?” General Hurlbut expressed confidence in holding his front all day - but stated that he was liable to be passed on the right or left at any time, and must in such a case fall back very promptly•. To General Hurlbut’s request for at least another brigade, General Grant answered that every man that would fight was in action then. General Grant further stated that he had no orders to give, further than to hold out to the last and do the best that could be done. He further stated that Lewis Wallace was under orders to move up, and that his fresh division coming up on the enemy’s flank, would restore the battle. The general commanding then rode off in the direction of the right wing."
So, Hurlbut heard from Grant in person that Wallace was expected to reach the battlefield over the Owl Creek bridge. On top of this, most of the participants who discussed this stated that Grant's orders sent Wallace to the right of the line, and throughout the day it seems that Grant and his staff were looking for Wallace on the right. River Road leads to the rear of the Union camps and it would be to the rear where they should have looked for Wallace.