it is all depend on the access privilage of the application and adminstion tools.
DBA can do any thing to the database. But it is not allow by the business rule. DBA should always insist not change individual data. It is also rule of DBA position.
In your case, that's all depend on how the the application is designed and applicaion access control.
Normally, production database system has log, which record every database operation(who,when and what). It is possible to restore the database status to a certain point of time. DBA will only do that when there is big issue.
In your case If DBA/manager/system admin change database data and remove all the log, u can do anothing with it. I don't think DBA dare to delete the back and log on production system.
I don't know what type of system you are using. And what level of privilage do u have. And the knowlege to find out the log and capebility to understand the log.
From you post, I don't think you are able to do it.
Why don't u just tell you boss you did apply leave at the time. Ask them trust you.
If they don't trust you and fake your record, you don't have to proof that you are right. Find another job, if you can.
Normally, you won't win when you fight with you boss by yourself( no one support you, for examle the boss's boss)