Your original premise was thw it was all based on the computer.
From your OP:
What did matter is that the computer told him that the third time through the batting order is fraught with peril--indeed, hopeless--no matter how well the starter is pitching. The computer also did not care that Anderson, the guy who came in, was tired and had an ERA of over 7 (which became 9) in this WS. And, if the computer didn't care, Kevin Cash didn't either. And neither does the Rays hierarchy. What was it Humphrey Bogart said near the end of the movie, The African Queen? "The Germans have their systems and they sticks to 'em."
Also - the title of the thread.
Situational awareness aside, do you think Cash lived and died by what his computer said? Or did he just make bad calls based on the previous outcomes and how he managed all season long?