I think the question boils down to do you believe the employee is obligated to disclose the backup issue within the responsibility of the employment contract? I would say no, since the entire creation of the software was not within the responsibility of the contract, why would the documentation of the backup issue be within it?

I think the situation is analogous to the company giving the employee a big unwarranted pay raise, and then the employee lazily not doing more work, then the company firing the employee, but then arguing that at a minimum, the company has a reasonable professional courtesy to give the employee hours for their vacation days, even though it isn't specified within the contract.