Finally, D still uses the identity of a high school girl in the original world, but that girl is supposed to have died and reincarnated elsewhere. Isn't it just strange that D would keep using the identity of a dead person when they crafted the identity of a living person to enjoy a human life and slack off in the first place? I guess there's plenty of work for the administrators in the first place so these inconsistencies slipped through.
It's more that, while the explosion and resulting deaths were the direct result of D's actions, knowing that would require investigation. If you just glanced at it, it would look like it was the Hero and Demon King doing something they shouldn't have been. Because she was
right there, D just handled the incident and basically covered up what happened.
Basically, the network breach was the direct result of one of the network admins, but because they caused the breach, they were immediately aware of it and edited the relevant logs so that it looked like it was caused by some users misusing the system, and then handled the clean-up. Anyone who actually examines the logs will immediately discover the tampering and figure out what actually happened, but since the mess is handled already and the damage was confirmed to be minimal, they simply moved on, possibly with some new policies in place to better monitor users.
In short, D is stupid and lazy and thinks that she is smarter than everybody else (when the reality is that everybody else just thinks that she's too stupid to actually get away with anything), and her plan for not getting caught relies
entirely on nobody actually investigating for themselves. In her mind, this is fine, because the only other person who knows is not an administrator, and she can easily keep them from ratting her out.
She is completely ignoring the fact that, while Kumoko/White is indeed not an administrator, she nonetheless has elevated privileges, including some that are normally reserved for admins, and while she may not be smarter than everyone else, she is certainly smarter than D.