I think you're right that this force could not have passed through Coffeeville, but they could have connected with the Coffeeville-Pontotoc road at some point between Coffeeville and Banner. And if the screening force was four regiments they could have easily swept aside any federal detachments in their path. Given that they had the direct road to Pontotoc while the main body took the long road through Houston, I don't see any reason why they couldn't have reached Pontotoc around the same time.
A lot is made of Grant's treatment of Murphy, but little is ever said about Grant's reaction to Mizener. He really seems to fail as a cavalry commander here, detecting only the screening force of four regiments, notifying Grant only after the Confederates have reached Pontotoc, and then only managing to make 29 miles in the direction of Holly Springs while Van Dorn's men rode over 40.