I have spoken to mathematician and many learned people and finally came to a conclusion:
The discrepancy came about because of ambiguity in the way formula is written! At the first place, Casio should have just reported "Syntax error".
First, 6÷2(1+2) is not the same as 6÷2*(1+2) from the way machine will interpret it.
In school, we always write 2(a+c) to mean 2a+2c. Thus, the answer became 6÷6=1. So the equation is actually:
Updates: My reader Brendan gave a link to support 9. This link looks at the whole situation from mathematical correctness! Worth reading.
From my logical thinking without bringing in all the "legality" point of view, 6÷2(1+2) is simply 6÷2(3)=9, ie, evaluating form left to right!
So, do you agree with the professor's argument from the link above?
For me, I am not concerned but just to remind ourselves that accuracy in entering formula into a machine is important. All this argument is academic which we leave it to the professors.