I hate to be the bearer of bad news, but I'm afraid that as an at-will employee your options are extremely limited.
As an at-will employee, you can be terminated at any time for any reason (even a false one) with or without any prior notice.
This stems from the employment at-will doctrine, which is codified in California Labor Code Section 2922, and states:
"An employment, having no specified term, may be terminated at
the will of either party on notice to the other. Employment for a
specified term means an employment for a period greater than one
Since an employer can terminate an employee for any reason, an employer can also discipline an employee for the same reasons, so you would not have a claim of retaliation against the individual who spurred on the investigations.
All that said, you have mentioned two very good points that you can and should bring up in your defense. 1) That you were trained differently and the people who trained you are now gone from the company; and 2) that you accidentally entered your time differently than it was. This would be greatly assisted if there are about the same number of entries giving you less time than you worked as more.
These would be good points to bring up in defending against termination and to bring up if you were terminated and your employer were to try to contest your application for unemployment benefits on this basis, although hopefully the latter will be irrelevant.
I sincerely XXXXX XXXXX had better news to give you (as I think the law is very unfair as it is currently written) but I hope you appreciate a direct and honest answer to your question.
Please let me know if you have any follow up questions.
If not, please ensure that you rate my answer positively so I get credit for my work.
Thanks and best of luck!