It never occurred to me that Kirk's presence in Engineering contributed to the accident.
I have always felt that there's something that Kirk did to contribute to the accident, but it may have been necessary. Sonak and Scotty and both told him that the Enterprise could not be ready in less than 20 hours, and he ordered that the 20-hour job be completed in 12 hours no matter what it took. When you force people to take shortcuts, accidents will happen.
The wormhole was also Kirk's fault, in the same sense. It's debatable whether Kirk was right or wrong to push so hard, but that pushing contributed to the wormhole and possibly to the transporter accident.