Deleting (I understood your use of burned, but just for those who aren't familiar with the setting I'm using a different term. I'll typically use burn to mean that a SIN has been discovered as fake) a SIN is possible, but it would require hacking into every SIN registry in the world which is typically only doable by powerful criminal organizations with access to a lot of resources. It's of course totally fine that D0 paid for the services of one of these organizations in her background, I bring it up because of the potential setting ties it could create should you so choose.
Edit: Though it does kind of seem like a case of wanting to have your cake and eat it, having a military background but dodging the consequences of it. Maybe a mercenary in a past life, as opposed to official military? I don't mind either way, just in a rambly mood at the moment.