Very interesting thought and post !
Thank you for posting it in our community ;).
I will just make a small footnote, if the notes are the transactions, then they cannot be "different" as in your example as on the Blockchain the nodes record the exact same transaction right?
Sincerely,
Yes the notes recorded by each student cannot differ from others else there is a disparity thus nullifying the evidence the the teacher wrote something in the first place.
If more than 51% of the nodes records a transaction then it can be accepted that the transaction really occur.. You must have heard of Satoshi's illustration of the three generals