What is the philosophical difference between an 'argument' that human minds following the laws of logic agree on "is correct" and a machine built by these minds

What is the philosophical difference between an 'argument' that human minds following the laws of logic agree on "is correct" and a machine built by these minds flashing a "correct light"? IMO the only advantage to be gained by introducing physical computers in the picture is lightning-fast book keeping. Why would you trust an Intel CPU, a Samsung SSD and a linux fs driver running some verifying framework more than the human brains designing, writing and executing said framework?